Question

A manufacturer of small appliances employs a market research firm to look into sales of its products. Shown below are last month's sales of electric can openers from a random sample of 50 stores. The manufacturer would like to know if there is convincing evidence in these data that the mean can opener sales for all stores last month was more than 22.

Sales
19
19
16
19
25
26
24
63
22
16
13
26
34
10
48
16
20
14
13
24
34
14
25
16
26
25
25
26
11
79
17
25
18
15
13
35
17
15
21
12
19
20
32
19
24
19
17
41
24
27

(1.) Set up the null and alternative hypotheses. Define the parameter in context.

(2.) First use Minitab or Excel to calculate the sample standard deviation, s. Then use the value of s to as many decimal places as you can to conduct the appropriate hypothesis test in Minitab. Report the value of the test statistic and p-value below.

Test statistic=

P-Value=

(3.) What is your decision using α = 0.05?

O reject Ho

O do not reject Ho

O accept Ho

(4.) State your conclusion in context.

Answer 1

(1) Ho: The mean sales is 22 or less (μ ≤ 22) and Ha: The mean sales in more than 22 (μ > 22)

(2) Sample standard deviation, s = 12.52289332

Data:    

n = 50   

μ = 22   

s = 12.52289332   

x-bar = 23.56   

Hypotheses:    

Ho: μ ≤ 22   

Ha: μ > 22   

Decision Rule:    

α = 0.05   

Degrees of freedom = 50 - 1 = 49

Critical t- score = 1.676550893   

Reject Ho if t > 1.676550893   

Test Statistic:    

SE = s/√n = 12.5228933215474/√50 = 1.771004558

t = (x-bar - μ)/SE = (23.56 - 22)/1.77100455754838 = 0.880856005

p- value = 0.191347994

Excel output:

(3) Since p- value > 0.05, fail to reject Ho

(4) Conclusion: There is no sufficient evidence that the mean sales is > 22

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