A factory fills bottles with a beverage, and each bottle is supposed to contain 500 Norah is in charge of a quality control test that involves measuring the amounts in a
sample of bottles to see if the sample mean amount is significantly different than 500
mL . She takes a random sample of 16 bottles and finds a mean amount of 497
mL
and a sample standard deviation of 6
Norah wants to use these sample data to conduct a test on the mean. Assume that all
conditions for inference have been met.
mL

Arecent study focused on the number of times men and women who live alone buy take-out dinner in a month. assume that the distributions follow the normal probability distribution and the population standard deviations are equal. the information is summarized below. statistic men women sample mean 24.85 21.33 sample standard deviation 5.54 4.93 sample size 34 36 at the 0.01 significance level, is there a difference in the mean number of times men and women order take-out dinners in a month? state the decision rule for 0.01 significance level: h0: μmen= μwomen h1: μmen ≠ μwomen. (negative amounts should be indicated by a minus sign. round your answers to 3 decimal places.) compute the value of the test statistic. (round your answer to 3 decimal places.) what is your decision regarding the null hypothesis? what is the p-value? (round your answer to 3 decimal places.)