Answer:
A) Null Hypothesis; H0: μ = 13.65
Alternative hypothesis; Ha: μ > 13.65
B) t = 1.42
C) The p-value is greater than the significance level of 0.05. Thus, we fail to reject the null hypothesis and conclude that there is insufficient evidence to support the claim that the mean transaction value is greater than $13.65.
D) type II error will be to conclude the average transaction value is equal to $13.65, in reality the average transaction value is greater than $13.65.
Step-by-step explanation:
We are given;
Population mean; μ = $13.65
Sample mean; x¯ = $14.92
Sample standard deviation; s = $5.51
Sample size; n = 38
DF = n - 1 = 38 - 1 = 37
Significance level; α = 0.05
A) The hypotheses is defined below;
Null Hypothesis; H0: μ = 13.65
Alternative hypothesis; Ha: μ > 13.65
B) Since we are given sample standard deviation, we will use formula for t-value. Formula for the test statistic is;
t = (x¯ - μ)/(s/√n)
t = (14.92 - 13.65)/(5.51/√38)
t = 1.42
C) From online p-value from t-score calculator attached, using; t = 1.42, α = 0.05, DF = 37, one tail, we have;
P-value = 0.08199
D) The p-value is greater than the significance level of 0.05. Thus, we fail to reject the null hypothesis and conclude that there is insufficient evidence to support the claim that the mean transaction value is greater than $13.65.
E) A type II error simply means accepting a null hypothesis that is not true.
Now, in this case what it will mean is to accept the null hypothesis.
Thus, type II error will be to conclude the average transaction value is equal to $13.65, in reality the average transaction value is greater than $13.65.
