Answer to Question #329255 in Statistics and Probability for krissy

Question

During the pandemic, online ordering of groceries and household supplies was offered by many stores as an accommodation for shoppers who preferred not to visit crowded stores in person. An online grocery shopping service claims that its mean delivery time is less than 120 minutes with a population standard deviation of 30 minutes. A random sample of 49 orders is delivered with a mean of 100 minutes. At the 95% confidence level, is there enough evidence to support the claim? Assume the data are normally distributed. Use the critical value method and respond to the prompts below.

Answer 1

Null hypothesis H0: µ ≥ 120

Alternative hypothesis H1 : µ<120

Level of significance: α= 0.05

Critical value: 1-α= 1-0.05=0.95

0.95 in z table= -1.645

The test statistics

x̅ =100

μ=120

σ =30

n =49

Compare Z calc to Z critical . In hypothesis testing, a critical value is a point on the test distribution compared to the test statistic to determine whether to reject the null hypothesis. Since

Z calc value is less than Z critical value and it is in the rejection region. Hence we can reject the null hypothesis.