FCQR 1100

Posted: August 26th, 2021

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FCQR 1100 End-of-Semester Assignment

1. Which of the following statement about a left- skewed distribution is correct?

Select one:

a. Median = Mean

b. Median > Mean

c. Mode = Median

d. None of these options

e. Median < Mean

2. Here is a set of data 12, 4, 5, 18, 11, 10, 8, 6, 5, 14, 11, 5, 3, 11, 5, 12. What are mean and median of the data set?

Select one:

a. Mean = 8.75, median = 9

b. Mean = 9, median = 10

c. Mean = 8.75, median 5.5

d. Mean = 9, median = 9

e. None of these options

3.In a job application form, the candidates need to fill in their expected salary. What is the level of measurement of this variable?

Select one:

a. Nominal

b. None of these options

c. Ordinal

d. Interval

e. Ratio

4.A study is conducted to determine the percentage of voters of a state would support the incumbent governor. What is the minimum sample size needed to estimate the population proportion with a margin of error of 0.05 or less at 90% confidence interval?

Select one:

a. 271.

b. 270.

c. 135.

d. 136.

e. 30.

5.In a class of 40 students, 3 students are randomly selected using simple random sampling method. The students are numbered from 1 to 40. With the random numbers 402584702742734832, which students are in the sample?

Select one:

a. 4, 2, 5

b. 402, 584 702

c. 40, 25, 27

d. 4, 0, 2

e. 40, 25, 84,

6. In a sample of 400 voters, 360 of them indicate that they favor the incumbent governor. On the other hand, it would like to estimate the 98% confidence interval of population voters who are not favoring the incumbent governor. So, the confidence interval would be

Select one:

a. 0.0651 to 0.1348

b. 0.8741 to 0.9294.

c. 0.1240 to 0.2808.

d. 0.0706 to 0.1294.

e. 0.7653 to 0.8351.

7.The officer of the Hong Kong Customs and Excise Department in the airport will randomly select passengers to examine their luggage. The officer usually randomly select one of every 50th passengers in the morning, one of every 40th passengers in the afternoon, and one of every 30th passengers in the evening for luggage examination. Which of the following sampling methods does the officer use?

Select one:

a. common sample

b. stratified sample

c. simple random sample

d. systematic random sample

e. random number sample

8.If X is distributed normally with mean of $100 and standard deviation of $50, what is the Z- score for X = $250?

Select one:

a. 2.3

b. 1.8

c. 3.0

d. 3.5

e. 1.5

9.A random sample of 64 students at a university showed an average age of 25 years and a sample standard deviation of 2 years. The 95% confidence interval for the true average age of all students in the university is

Select one:

a. 23.0001 to 27.0001.

b. 24.6000 to 25.3900.

c. 24.5004 to 25.4996.

d. 19.3403 to 29.2302.

e. 21.0001 to 23.4002.

10.In sampling with replacement a sampling unit can be selected ______.

Select one:

a. More than one time

b. Twice

c. Less than one time

d. Only once

e. No restriction

12.____ involves the collection, presentation, and characterization of a set of data in order to properly describe the various features of these data.

Select one:

a. Descriptive statistics

b. Inferential statistics

c. Sampling method

d. Summarization

e. Independent statistics

13.In a clinic, the nurse will measure the body temperature of each patient who come to see the doctor. What is the level of measurement of this variable?

Select one:

a. None of these options

b. Ratio

c. Interval

d. Nominal

e. Ordinal

14.In general, the expected frequencies per cell in the conduct of a Chi-Square test are those one would

Select one:

a. expect to find in a given cell if the null hypothesis were actually false

b. expect to find in a given cell if the null hypothesis were actually true

c. expect to find in a given cell if the alternative hypothesis were actually false

d. expect to find in a given cell if the alternative hypothesis were actually true

e. expect to find in a given cell if either the null hypothesis or the alternative hypothesis were actually true

15.In order to determine an interval for the mean of a population with unknown standard deviation, a sample of 81 items is selected. The mean of the sample is determined to be 36. The associated number of degrees of freedom for reading the t value is

Select one:

a. 80.

b. 81.

c. 8.

d. 82.

e. 9.

16.A statement made about a population for testing purpose is called:

Select one:

a. Statistic

b. One tailed test

c. Test-Statistic

d. Hypothesis

e. Level of Significance

17.Here is a data set 7, 8, 4, 5, 16, 20, 20, 24, 19, 30, 23, 30, 25, 19, 29, 29, 30, 30, 40, 56. The first quartile (Q1) and third quartile (Q3) of the data set are:

Select one:

a. Q1 = 14, Q3 = 30

b. Q1 = 16, Q3 = 28

c. Q1 = 16, Q3 = 30

d. Q1 = 15, Q3 = 29

e. None of these options

18.Our colleague group claims that on average, they have to travel for at least 22 minutes in order to go back to office each day. 30 colleagues are asked about their travelling time and the sample had a mean of 21.2 minutes and a standard deviation of 3.3 minutes. If the hypothesis test is performed at 0.01 level of significance, which of the following is the critical value used in the hypothesis testing?

Select one:

a. 1.6449

b. 1.9600

c. -2.5758

d. None of these options

e. -2.3263

19.You should be careful about using a chi-square test when

Select one:

a. the obtained frequencies are quite big.

b. the expected frequencies are quite small.

c. the obtained frequencies are quite small.

d. the expected frequencies are different across the categories.

e. None of these options

20.A fitness club has interviewed 50 people with age between 20 and 30 to study exercise habits among young people. They are asked about their exercise habits, such as frequency, duration, and form. What is the data collected from these 50 people?

Select one:

a. The sample data

b. The secondary data

c. The qualitative data

d. The quantitative data

e. The population data

21.Which one is the correct description of interquartile range (IQR)?

Select one:

a. None of these options

b. IQR is the midspread in the middle 75% of the data

c. IQR is affected by outliers

d. IQR measures the spread in the middle 50% of the data

e. IQR is the midspread in the middle 25% of the data

22.Which of the following is/ are included in a boxplot for a given set of data?

Select one:

a. All of these options

b. The third quartile

c. The first quartile

d. The median

e. The largest value of data

23.If a population had 175 objects in it, and we wanted to take a sample of 35 of those objects using systematic random sampling, what would our interval size be?

Select one:

a. 5

b. 175

c. 100

d. 140

e. 35

24.The owner of a local nightclub has recently surveyed a random sample of 250 customers of the club. She would now like to determine whether or not the mean age of her customer is over 35. Suppose that the population standard deviation is known. If the hypothesis test is performed at 0.01 level of significance, what rejection region should be use?

Select one:

a. We reject the null hypothesis if the test statistic < -2.3263

b. We reject the null hypothesis if the test statistic < -2.5758

c. None of these options

d. We reject the null hypothesis if the test statistic > 2.5758

e. We reject the null hypothesis if the test statistic > 2.3263

25.Given a set of sample data be 25, 38, 40, 65, 36, 46, 54, 62. What are the range, mean and the sample standard deviation (SD)?

Select one:

a. range= 50, mean = 48.85, SD = 12.6533

b. range= 40, mean = 48.85, SD = 13.7399

c. range= 40, mean = 45.75, SD = 13.7399

d. None of these options

e. range= 50, mean = 45.75, SD = 12.6533

26.Which of the following is a measure of variation?

Select one:

a. Mean

b. Quartile

c. None of these options

d. Mode

e. Standard Deviation

Given a set of data be 6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49. What are the first quartile (Q1) and the third quartile (Q3)?

Select one:

a. None of these options

b. Q1 = 17, Q3 = 45

c. Q1 = 15, Q3 = 43

d. Q1 = 18, Q3 = 47

e. Q1 = 14, Q3 = 42

28.The first quartile (Q1), median (Q2) and third quartile (Q3) are identified in a set of data. It is determined that Q3 > Q2 > Q1. What is the distribution of the data set?

Select one:

a. None of these options

b. Left-skewed

c. Not enough information to determine the skewnes of distribution

d. Symmetric

e. Right-skewed

29.A teacher wants to randomly select 8 male and 10 female students from his class to join the school choir team. Which of the following sampling methods should be used?

Select one:

a. stratified sample

b. systematic random sample

c. random number sample

d. simple random sample

e. common sample

30.In case of estimating a confidence interval for population mean or proportion, when the sample size increases, the margin of error

Select one:

a. fluctuates depending on the mean.

b. None of the above.

c. stays the same.

d. increases.

e. decreases.

(a) A study is to be carried out that requires 80% confidence of estimating the proportion of students who study over 3 hours per day to within ±0.200±0.200. How large the sample size of students should be for such estimation?

The critical value is Answer [correct to 4 decimal places].

According to the formula [select one below]

x¯±zσ/n−−√x¯±zσ/n

n=p(1−p)(z/e)2n=p(1−p)(z/e)2

p±zp(1−p)/n−−−−−−−−−√p±zp(1−p)/n

x¯±ts/n−−√x¯±ts/n

n=(z/e)2/4n=(z/e)2/4

n=(zσ/e)2n=(zσ/e)2

the required sample size is at least Answer [correct to 2 decimal places].

Therefore, the required sample size is Answer.

(b) A researcher plans to estimate the mean score of statistics exam of a population of students to within ±17±17 marks at 99% confidence level. The standard deviation of the examination score of the population is 17.86. What is the sample size required?

The critical value is Answer [correct to 4 decimal places].

According to the formula [select one below]

p±zp(1−p)/n−−−−−−−−−√p±zp(1−p)/n

n=p(1−p)(z/e)2n=p(1−p)(z/e)2

n=(zσ/e)2n=(zσ/e)2

x¯±ts/n−−√x¯±ts/n

x¯±zσ/n−−√x¯±zσ/n

n=(z/e)2/4n=(z/e)2/4

the required sample size is at least Answer [correct to 2 decimal places].

Therefore, the required sample size is Answer.

(c) A research company wants to estimate the percentage of citizens of a city who are willing to invest in real estate in the coming 2 years, and will declare that the real estate market is shrinking if this percentage is lower than 26%. In a survey among 1200 citizens, 302 of them are willing to invest within 2 years. Construct a 90% confidence interval for the proportion of the citizens of that city who are willing to invest in real estate in the coming 2 years and briefly comment on the real estate market.

The Answer population sample  proportion is Answer [give an answer between 0 and 1 correct to 4 decimal places].

The critical value is Answer [correct to 4 decimal places].

According to the formula [select one below]

n=(z/e)2/4n=(z/e)2/4

n=(zσ/e)2n=(zσ/e)2

p±zp(1−p)/n−−−−−−−−−√p±zp(1−p)/n

x¯±zσ/n−−√x¯±zσ/n

x¯±ts/n−−√x¯±ts/n

n=p(1−p)(z/e)2n=p(1−p)(z/e)2

the confidence interval is: Answer ≤π≤≤π≤ Answer

According to the confidence interval, although the Answer sample mean population proportion population mean sample proportion  is Answer more less  than Answer [give an answer between 0 and 1 here], the research company Answer is not is  Answer% confident that the Answer population mean population proportion sample mean sample proportion  of citizens who are willing to invest in real estate in the coming 2 years is truly Answer above below  Answer. Therefore, the research company Answer should should not  declare that the real estate market in this city is shrinking.

(d) The manager of a singing agency wants to know the customer spending on CD on their singers. It is believed that it is a good result if customers would spend at least an average of $1000. A random sample of 17 customers is selected. The spending data on CD (in dollars) are listed below:

    1     1045     1286     624     139     1185     161     583     593     384     489     951     263     642     223     520     283

Use the given data to construct a 95% confidence interval estimate of the mean spending on CD on their singers and briefly comment and suggest on the spending of the customers on the singers.

The mean and standard deviation of the data are Answer and Answer, respectively [correct to 4 decimal places].

The critical value is Answer [correct to 4 decimal places].

According to the formula [select one below]

n=(zσ/e)2n=(zσ/e)2

n=(z/e)2/4n=(z/e)2/4

x¯±zσ/n−−√x¯±zσ/n

x¯±ts/n−−√x¯±ts/n

n=p(1−p)(z/e)2n=p(1−p)(z/e)2

p±zp(1−p)/n−−−−−−−−−√p±zp(1−p)/n

the confidence interval is: Answer ≤μ≤≤μ≤ Answer

According to the confidence interval, the manager is Answer% confident that the Answer population proportion sample mean sample proportion population mean  spending is Answer more less  than Answer. Therefore, the mean spending of customers Answer does not meet meets  the expectation of the company and the singing agency Answer should need not  think of more promotion on their singers in selling CD.

a) In the past, credit card customers spent $2792 on average. To investigate whether the recent change of economy has affected the spending of the credit card customers, a marketing department of a bank selects a random sample of 81 customers for a survey. Based on the survey result, it is found that the selected customers are spending $2734 on average with a standard deviation of $482. At 1% level of significance, is there any evidence to conclude that the spending of the credit card customers has decreased?

The Answer false alternative true null  hypothesis H0 in this test is:

μ≤2734μ≤2734

X¯≥2734X¯≥2734

μ>2792μ>2792

μ=2734μ=2734

μ>2734μ>2734

μ≤2792μ≤2792

μ=2792μ=2792

X¯=2734X¯=2734

μ≥2734μ≥2734

X¯≥2792X¯≥2792

μ<2734μ<2734

X¯=2792X¯=2792

X¯>2792X¯>2792

μ≠2734μ≠2734

X¯≤2734X¯≤2734

μ≥2792μ≥2792

μ<2792μ<2792

X¯≠2734X¯≠2734

X¯>2734X¯>2734

X¯≠2792X¯≠2792

X¯<2792X¯<2792

μ≠2792μ≠2792

X¯≤2792X¯≤2792

X¯<2734X¯<2734

and the Answer true alternative null false  hypothesis H1 is:

X¯=2792X¯=2792

X¯<2792X¯<2792

μ≥2734μ≥2734

μ>2792μ>2792

X¯<2734X¯<2734

X¯≥2792X¯≥2792

μ≥2792μ≥2792

μ<2792μ<2792

μ<2734μ<2734

μ>2734μ>2734

X¯=2734X¯=2734

μ≠2734μ≠2734

X¯≠2734X¯≠2734

μ≠2792μ≠2792

μ≤2792μ≤2792

X¯>2734X¯>2734

X¯≥2734X¯≥2734

X¯≠2792X¯≠2792

X¯≤2734X¯≤2734

μ≤2734μ≤2734

μ=2734μ=2734

μ=2792μ=2792

X¯≤2792X¯≤2792

X¯>2792X¯>2792

The Answer level of significance level of confidence power of the test  αα = Answer [give a value between 0 and 1 correct to 4 decimal places].

The Answer population size sampling rate sample size  nn = Answer.

The chosen test statistic is:

t=(X¯−μ)/(S/n−−√)t=(X¯−μ)/(S/n)

Z=(X¯−μ)/(σ/n−−√)Z=(X¯−μ)/(σ/n)

Z=(p−π)/π(1−π)/n−−−−−−−−−√Z=(p−π)/π(1−π)/n

χ2=∑(fo−fe)2/feχ2=∑(fo−fe)2/fe

t=(r−ρ)/(1−r2)/(n−2)−−−−−−−−−−−−−√t=(r−ρ)/(1−r2)/(n−2)

and the test should be a Answer two-tail lower-tail upper-tail  test.

The critical value is Answer [give a positive value correct to 4 decimal places].

The decision rule is then:

    Reject Answer H1 H0  if Answer -critical value < test statistic < critical value test statistic = critical value OR test statistic = -critical value test statistic = critical value test statistic > critical value OR test statistic < -critical value test statistic NOT= critical value test statistic > critical value test statistic < -critical value ;

    Do not reject Answer H1 H0  otherwise.

From the given data, the test statistic is found to be Answer [correct to 4 decimal places].

Hence, Answer H0 is not rejected H0 is rejected H1 is not rejected H1 is rejected  and there is Answer insufficient sufficient  evidence that the spending of the credit card customers has Answer changed unchanged increased decreased  at the 0.01 level of significance.

(b) A mobile phone company has a new design of smart phone and wants to investigate how customers of different age groups feel about the proposed new design. A market research survey is conducted and the responses are shown in the table below:

Like the designDislike the designAge <21169Age 21−351914Age >354227Age <21Age 21−35Age >35Like the design161942Dislike the design91427

At the 0.10 level of significance, is there evidence of a significant difference in the feeling about the new design among the three age groups?

H0: The Answer proportions of “like the design” among the three “age groups” “proportion of dislike the design” and “age group” “proportion of like the design” and “age group” proportions of “like the design” and “dislike the design” “feeling about the new design” and “age group” feelings of “like the design” and “dislike the design” proportions of “dislike the design” among the three “age groups”  Answer are not are  independent.

H1: The Answer “feeling about the new design” and “age group” proportions of “like the design” and “dislike the design” “proportion of like the design” and “age group” feelings of “like the design” and “dislike the design” proportions of “dislike the design” among the three “age groups” proportions of “like the design” among the three “age groups” “proportion of dislike the design” and “age group”  Answer are are not  independent.

The Answer level of significance power of the test level of confidence  αα = Answer [give a value between 0 and 1 correct to 4 decimal places].

The Answer population size sampling rate sample size  nn = Answer.

The chosen test statistic is:

Z=(X¯−μ)/(σ/n−−√)Z=(X¯−μ)/(σ/n)

t=(X¯−μ)/(S/n−−√)t=(X¯−μ)/(S/n)

χ2=∑(fo−fe)2/feχ2=∑(fo−fe)2/fe

t=(r−ρ)/(1−r2)/(n−2)−−−−−−−−−−−−−√t=(r−ρ)/(1−r2)/(n−2)

Z=(p−π)/π(1−π)/n−−−−−−−−−√Z=(p−π)/π(1−π)/n

and the test should be Answer two-tail lower-tail upper-tail  test.

The critical value is Answer [give a positive value correct to 4 decimal places].

The decision rule is then:

    Reject Answer H0 H1  if Answer test statistic NOT= critical value -critical value < test statistic < critical value test statistic = critical value OR test statistic = -critical value test statistic > critical value OR test statistic < -critical value test statistic < -critical value test statistic > critical value test statistic = critical value ;

    Do not reject Answer H0 H1  otherwise.

From the given data, the expected frequencies can be calculated using Answer row total*column total/n (row total-column total)/n (column total-row total)/n column total*n/row total (row total+column total)/n row total*n/column total  and are shown in the table below:

	Age < 21	Age 21 – 35	Age > 35	TOTAL
Like the design	Answer	Answer	Answer	Answer
Dislike the design	Answer	Answer	Answer	Answer
TOTAL	Answer	Answer	Answer	Answer

Hence, the test statistic is found to be Answer [correct to 4 decimal places].

Consequently, Answer H0 is not rejected H1 is not rejected H0 is rejected H1 is rejected  and there is Answer sufficient insufficient  evidence that the Answer “proportion of dislike the design” and “age group” proportions of “like the design” among the three “age groups” “proportion of like the design” and “age group” “feeling about the new design” and “age group” proportions of “dislike the design” among the three “age groups” proportions of “like the design” and “dislike the design” feelings of “like the design” and “dislike the design”  Answer are not are  independent at the 0.10 level of significance.

(c) What is significance level? What is the role of significance level in hypothesis testing?

Significance level is the probability of committing Answer Type I Type II Type III  error, i.e., the probability of Answer not rejecting a true null hypothesis rejecting a true alternative hypothesis not rejecting a true alternative hypothesis rejecting a false null hypothesis not rejecting a false alternative hypothesis rejecting a true null hypothesis rejecting a false alternative hypothesis not rejecting a false null hypothesis . Significance level is used to determine Answer whether a test is one-tail or two-tail H0 and H1 the critical value the test statistic the degree of freedom . The smaller the significance level, the Answer stronger weaker  the evidence is needed to reject the null hypothesis.