Question

1. 14-18) Vendingmachinesonacollegecampusofferavarietyofsnacks.Thepurchasingagentbelievesthateachtypeofsnackisequallypreferredbystudentsandconsequentlyordersequalquantities.Thenumberofsnackssoldfromvendingmachinesonthiscampusforthelastsixmonthsisshowninthefollowingtable.

SnackType	Chips	CandyBars	Crackers	Nuts
PurchaseFrequency	159	218	174	149

        

         What type of test should we perform to test the agent’s belief?

1. Homogeneity Test
2. Independence Test
3. Goodness-of-fit Test
4. Two-sided t test
5. Two-sided test for proportions

2. If there is no seasonal effect on human births, we would expect equal numbers of children to be born in each season (winter, spring, summer, and fall). A student takes a census of her statistics class and finds that of the 120 students in the class, 25 were born in winter, 35 in spring, 32 in summer, and 28 in fall. She wonders if the excess in the spring is an indication that births are not uniform throughout the year.

The p-value for the chi-square statistic is 0.021. At the significance level of 0.05, the correct decision and conclusion are (is):

I.    Fail to reject the null hypothesis that the births are uniform throughout the year.

II.  Reject the null hypothesis that the births are not uniform throughout the year.

III.There is sufficient evidence that the births are not uniform throughout the year.

IV.There is not sufficient evidence that the births are not uniform throughout the year.

A)  III only

B)  Both II and III

C)  Both I and IV

D)  I only

E)  II only

3. An analyst at a local bank wonders if the age distribution of customers coming for service at his branch in town is the same as at the branch located near the mall. He selects 100 transactions at random from each branch and researches the age information for the associated customer. Here are the data:

	Age
	Less than 30	30-55	56 or older	Total
In-Town Branch	20	40	40	100
Mall Branch	30	50	20	100
Total	50	90	60	200

       What type of test are you performing?

1. Goodness-of-fit Test
2. Homogeneity Test
3. Independence Test
4. Two-sample t test among independent groups
5. Two-sample t test for paired data

4. An analyst at a local bank wonders if the age distribution of customers coming for service at his branch in town is the same as at the branch located near the mall. He selects 100 transactions at random from each branch and researches the age information for the associated customer. Here are the data:

	Age
	Less than 30	30-55	56 or older	Total
In-Town Branch	20	40	40	100
Mall Branch	30	50	20	100
Total	50	90	60	200

What is the expected number of less-than-30-year-old customers coming for service at the branch located near the mall?

1. 25
2. 45
3. 30
4. 40
5. 50

5. An analyst at a local bank wonders if the age distribution of customers coming for service at his branch in town is the same as at the branch located near the mall. He selects 100 transactions at random from each branch and researches the age information for the associated customer. Here are the data:

	Age
	Less than 30	30-55	56 or older	Total
In-Town Branch	20	40	40	100
Mall Branch	30	50	20	100
Total	50	90	60	200

The p-value for the chi-square statistic is 0.231. At the significance level of 0.05, the correct decision and conclusion are (is):

1. Fail to reject the null hypothesis that the age distribution of customers coming for service at is the same as at both branches.
2. Reject the null hypothesis that the age distribution of customers coming for service at is the same as at both branches.
3. There is sufficient evidence that the age distribution of customers coming for service at is not the same as at both branches.
4. There is not sufficient evidence that the age distribution of customers coming for service at is not the same as at both branches.

1. III only
2. Both II and III
3. Both I and IV
4. I only
5. IV only

Answer 1

14. To check if the observed frequency is different from expected frequencies, chi-square goodness of fit test should be conducted.
c) Goodness of fit test is correct

15. The null hypothesis is that the births are uniform throughout the year.
As p = 0.021, the null hypothesis is rejected.

Hence, there is sufficient evidence that the births are not uniform throughout the year.
A) III only is correct.

16. Here, we need to check the dependence between two variables - age and branch
C) Independence test is corrrect

17. Expected number of less than 30 year old customers at mall branch = 50*100/200 = 25
Hence, A) 25 is correct.

18. The p-value = 0.231, we fail to reject the null hypothesis that the variables are independent of each other.
Hence, I and IV is correct.

C) option is correct.