A consumer advocacy group suspects that a local supermarkets 10-ounce packages of cheddar cheese actually weigh less than 10 ounces. The group took a random sample of 50 packages and found that the mean weigh for the sample was 9.955 ounces. The population follows a normal distribution with the population standard deviation of .15 ounce.

Is there a statistically significant difference in the mean weighs of 10-ounce packages in the sample compared to the labeled amount of 10-ounces?

What does "statistically significance" mean in the relation of this question?

Why isn't it enough to say that "since the mean weight in the sample is less than 10 ounces, it is clear that the labeling is incorrect?

Construct a hypothesis test for this question.

Perform the hypothesis test analysis for a significance level of 1% using the critical-value approach (Test Statistic comparison)

What is the p-value for this test? Will you reject the null hypothesis at?