Question

A local hardware store claims that the mean waiting time in line is less than 3.5 minutes. A random sample of 20 customers has a mean of 3.3 minutes with a standard deviation of 0.8 minute. If a = 0.05, test the store's claim. Assumption: ? Parameter: ? Hypothesis: ? Test Statistic: ? Reject- Region: ? Calculated Test Statistic: ? Conclusion: ? P-value: ?

Answer 1

Assumption:
the sample is randomly selected from normally distributed population

Parameter: Mean

Below are the null and alternative Hypothesis,
Null Hypothesis: μ = 3.5
Alternative Hypothesis: μ < 3.5

Rejection Region
This is left tailed test, for α = 0.05 and df = 19
Critical value of t is -1.729.
Hence reject H0 if t < -1.729

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (3.3 - 3.5)/(0.8/sqrt(20))
t = -1.118

P-value Approach
P-value = 0.1388
As P-value >= 0.05, fail to reject null hypothesis.

There is not sufficient evidence to conclude that the mean is less than 3.5