Question

An analyst collected data from 25 randomly selected transactions and found the purchase amounts​ (in $). The mean is $22.13 and the standard deviation is ​$13.42 The analyst wants to know if the mean purchase amount of all transactions is at least $17.

36.07
23.25
22.62
17.78
45.82
47.76
31.97
6.77
42.95
10.89
13.11
5.96
28.56
15.29
16.19
6.88
4.74
18.33
10.07
18.02
8.68
35.77
41.98
16.66
27.11

​a) What is the null​ hypothesis?

b) Is the alternative​ one- or​ two-sided?

c) What is the value of the test​ statistic?

​d) What is the​ P-value of the test​ statistic?

​e) What do you conclude at alpha α=0.05?

The​ P-value is less than/ greater than alphaα​, so fail to reject/ reject the null hypothesis. There is sufficient/ insufficient evidence to conclude that the mean purchase amount of all transactions is greater than $22.

Answer 1

a)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 22

b)

Alternative Hypothesis, Ha: μ > 22

one sided

c)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (22.13 - 22)/(13.42/sqrt(25))
t = 0.048

d)

P-value Approach
P-value = 0.4811

e)

As P-value >= 0.05, fail to reject null hypothesis.

The​ P-value is greater than alphaα​, so fail to reject null hypothesis. There is insufficient evidence to conclude that the mean purchase amount of all transactions is greater than $22.