Question

Supermarkets have limited the number of customers who are in their stores at any one time. At one particular store, store managers decide that 100 customers at one time is necessary to ensure social distancing guidelines mandated by the government. One store manger suspects that the number of customers is more than 100 so he counts the number of customers for a week at different times of the day and on different days of the week. Here are the numbers: 105, 98, 111, 123, 88, 95, 109. Using the choices shown below fill in the blanks by typing the appropriate letter for your choices: (type your answer on the blank)

Explain your conclusion in context:

The is Blank 1 (sufficient/insufficient) evidence that the Blank 2 (mean/proportion/correlation) of the  number of store customers per week is Blank 3 (greater than/less than, equal to) 100.

Answer 1

We need to conduct a one sample t-test to check that whether the mean number of store customers per week is more than 100.

Ho: u <= 100

Ha: u > 100

The sample statistic is:

X = Sample Mean = 104.14
s = Standard deviation = 11.61
n = Sample size = 7

The formula for t-statistic is:

Inputting the values,

t = (104.14 - 100) / (11.61/√7)

t = 0.944

df = n - 1 = 6

p-value = 0.1908 (one-tailed)

As the p-value > 0.05, we fail to reject the null hypothesis.

Conclusion:

There is insufficient evidence that the mean of the number of store customers per week is greater than 100.