Question

4. The owner of specialty coffee shop wants to study coffee purchasing habits of customers at her shop. She selects a random sample of 60 customers during certain week, with the following results:

The amount spent was ? = $7.25, S = $1.75

Thirty-one customers say they definitely will” recommend the specialty coffee shop to family friends.

a. At the 0.05 level of significance, is there evidence that the population mean amount spent was different from $6.50?

b. Determine the p-value in (a).

c. At the 0.05 level of significance, is there evidence that more than 50% of all customers say they “definitely will” recommend the specialty coffee shop to family and friends?

d. What is your answer to (a) if the sample mean equals $6.25?

e. What is your answer to (c) if 39 customers say they “definitely will” recommend the specialty coffee to family and friends?

f. Submit an excel file which clearly describes the data, intermediate calculations, and final results. Also submit a word file to provide explanation of each step while solving the problems.

Answer 1

a ) Here we want to test " Wether there is evidence that the population mean amount spent was different from $6.50"

So null hypothesis ( H₀ ) and the alternative hypothesis ( H_a ) is as follows :

Here population standard deviation is not given and we use sample standard deviation(s) instead of population standard deviation ( ). Also sample size is sufficiently large( >= 30) so we can used one sample t confidence interval for population mean( )

Using Minitab:

n = sample size = 60

= sample mean = 7.25

s = sample standard deviation = 1.75

Step 1) Click on Stat>>>Basic Statistics >>1 sample t...

Step 2) Select summarized data

Sample size : 60

Mean: 7.25

Standard deviation : 1.75

then click on Perform hypothesis test enter hypothesis mean ( 6.50)

Step 3)then click on Option select level of confidence = 1 - alpha = 1 - 0.05 = 0.95

So put it as 95

Alternative "not equal"

Click on OK

again Click on Ok

So we get the following output

b) P -value = 0.002

Decision rule:

1) If p-value < level of significance (alpha) then we reject null hypothesis

2) If p-value > level of significance (alpha) then we fail to reject null hypothesis.

Here p value < 0.05 so we used first rule.

That is we reject null hypothesis

d ) Conclusion: At 5% level of significance there are sufficient evidence to say that there is evidence that the population mean amount spent was different from $6.50.