Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. the executives hire a statistical consultant and ask her to determine the mean shopping time(mu) of customers at the supermarkets. the consultant will collect a random sample of shopping times at the supermarkets and use the mean of these shopping times to estimate (mu). assuming that the standard deviation of the population of shopping times at the supermarkets is 26 minutes, what is the minimum sample size she must collect in order for her to be 95% confident that her estimate is within 5 minutes of (mu)?

The formula to calculate the sample size is:

n = Z number * standard deviation/ confidence estimate)^2

The z number for 95% confidence is 1.96

The standard deviation is given as 26 minutes.

The confidence estimate is given as 5 minutes.

The sample size is: (1.96 * 26/5)^2 = 103.87 = 104 shoppers.

a. People with less religious backgrounds engage in less altruistic behavior than people with nonreligious histories, or there is no difference between the groups with respect to altruistic behavior.

Correct, that's what we try to proof, and on this case this statement present how we need to put the null hypothesis and we have the key word "there is no difference" that is important to use when we create the null hypothesis for this type of test.

Step-by-step explanation:

Previous concepts

The null hypothesis attempts "to show that no variation exists between variables or that a single variable is no different than its mean"

The alternative hypothesis "is the hypothesis used in hypothesis testing that is contrary to the null hypothesis"

Solution to the problem

We want to proof that "people with religious backgrounds engage in more altruistic behavior than nonreligious people"

Assuming that we have the following options, we select one based on the info provided.

a. People with less religious backgrounds engage in less altruistic behavior than people with nonreligious histories, or there is no difference between the groups with respect to altruistic behavior.

Correct, that's what we try to proof, and on this case this statement present how we need to put the null hypothesis and we have the key word "there is no difference" that is important to use when we create the null hypothesis for this type of test.

b. People with religious backgrounds are more altruistic than people with nonreligious backgrounds.

That's not at all False, but the problem is that we don't specify if we have differences or not betwen the two groups, for this case is not the best answer.

c. People with nonreligious backgrounds are more altruistic than people with religious backgrounds.

That's not true since we are trying to proof the inverse statement. "people with religious backgrounds engage in more altruistic behavior than nonreligious people"

d. There would be no null hypothesis for this experiment.

False that's not correct, we have a null and alternative hypothesis for this case.