A researcher wants to determine whether shoppers will spend more money at the gr

Question

A researcher wants to determine whether shoppers will spend more money at the grocery when they use a credit card to pay for their groceries rather than cash. In which situation could the researcher use a hypothesis test for matched pairs?

a. The researcher asks the people in the sample whether they prefer to shop for their groceries using a credit card more than with cash (yes/no).

b. The people in the experiment are told to use only cash for their grocery shopping for one trip and report how much money they spent. The next trip, the same people in the sample use only credit cards for their grocery shopping and calculate the total. The researcher compares the total spent by each individual to see if they spent more, on average, when using cash or the credit card.

c. The researcher randomly assigns half of the sample to only use cash for their grocery shopping for one trip to the grocery store. The other half of the sample uses only credit cards. The researcher compares the amount of money spent by each of the two groups.

2. The local power company is testing a new type of thermostat that automatically changes the air conditioning settings on “peak days” to see if using the new thermostat will reduce power consumption. The power company randomly selects 35 homes of a similar size to test the new thermostat. They compare the average summer power consumption before and after the new thermostat is installed. The power company wishes to find out if there is evidence to suggest that energy use was significantly higher before the new thermostats were installed (with lower energy use after the new thermostats were installed).

Given the design of the study and the question of interest, which one of the following four computer outputs is relevant to use?

3.

The director of a daycare center noticed that the infants were getting more diaper rashes than usual in the summer time. The policy of the center was to change the diapers on a schedule every three hours. The director wanted to find out if adjusting the diaper-changing schedule to every two hours would significantly reduce the number of diaper rashes. Since some of the infants seemed to have more sensitive skin, she decided to directly compare the number of diaper rashes for each individual infant when the diaper was changed every three hours versus every two hours. For the first week, the daycare center changed the diapers as usual every three hours and noted the number of days that each infant had symptoms of a diaper rash. During the second week, the teachers changed diapers every two hours and recorded the number of days with symptoms of a diaper rash. At the end of the two weeks, they compared for each individual infant the number of days with symptoms of a diaper rash when the diapers were changed every three hours versus every two hours.

Let 1 and 2 represent the mean number of days with symptoms of a diaper rash when diapers were changed every three hours and two hours, respectively, and let d be the mean of the differences in the number of days with symptoms of a diaper rash (diaper rash days when changed every three hours minus diaper rash days when changed every two hours).

Which of the following are the appropriate null and alternative hypotheses?

A. H0: d = 0

Ha: d > 0

b. H0: d = 0

Ha: d < 0

c. H0: d > 0

Ha: d = 0

D. H0: 1= 2

Ha: 1 > 2

4. The director of a daycare center noticed that the infants were getting more diaper rashes than usual in the summer time. The policy of the center was to change the diapers on a schedule every three hours. The director wanted to find out if adjusting the diaper-changing schedule to every two hours would significantly reduce the number of diaper rashes. Since some of the infants seemed to have more sensitive skin, she decided to directly compare the number of diaper rashes for each individual infant when the diaper was changed every three hours versus every two hours. For the first week, the daycare center changed the diapers as usual every three hours and noted the number of days that each infant had symptoms of a diaper rash. During the second week, the teachers changed diapers every two hours and recorded the number of days with symptoms of a diaper rash. At the end of the two weeks, they compared for each individual infant the number of days with symptoms of a diaper rash when the diapers were changed every three hours versus every two hours.

The following hypotheses were tested:

H0: d = 0

Ha: d > 0

The following is the (edited) output for the test:

Which of the following is an appropriate conclusion based on the output?

a. The data provide sufficient evidence to reject H0 and, thus, conclude that the mean number of days with diaper rash symptoms when changed every three hours is higher than the mean number of days with diaper rash symptoms when changed every two hours.

b. The data provide sufficient evidence to reject H0.We therefore conclude the data do not provide evidence to conclude that the mean number of days with diaper rash symptoms when changed every three hours is higher than the mean number of days with diaper rash symptoms when changed every two hours.

c. The data do not provide sufficient evidence to reject H0. We therefore conclude that the mean number of days with diaper rash symptoms when changed every three hours is higher than the mean number of days with diaper rash symptoms when changed every two hours.

d. The data do not provide sufficient evidence to reject H0. In other words, based on the data we cannot conclude that the mean number of days with diaper rash symptoms when changed every three hours is higher than the mean number of days with diaper rash symptoms when changed every two hours.

Explanation / Answer

4. The p value is less than alpha=0.05, reject H0. Therefore, option a)

3. H0: mud=0 (mean difference in number of days with symptoms of rash between change in diaper for 3 hours and 2 hours is 0)

H1: mud >0 mean difference in number of days with symptoms of rash between change in diaper for 3 hours is greater than 2 hours is 0)

ans (a)

2. Since the power company comapred average summer power consumption for household before and after installation of new thermostat, therefore, t test of mean difference is appropriate.

1. b) Here, same sample were once asked to use cash for shopping in on etrip and then credit for shopping in another trip to the crocery store.

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