Aresearcher believes that women today weigh less than in previous years. to investigate this belief, she randomly samples 41 women and records their weights. the scores have a mean of 111 lbs and a standard deviation of 12.4. a local census indicated that an earlier population has a mean weight of 115 lbs.
using an alpha of 0.01 one tail, the critical value of the appropriate statistic for testing the null hypothesis is:

The critical value of the appropriate statistic for testing the null hypothesis is -0.322

Step-by-step explanation:

First we must define the Null Hypothesis

H0: Miu >= 115

Ha: Miu < 115

The null hypothesis is that the population mean Miu of weights of women is greater or equal than the one of previous years, 115 lbs. We define the hypothesis so that, if we reject the Null Hypothesis H0, we will prove what we want, that weights of women are less.

As our sample is greater than 30 observations, we can use the Central Limit Theorem and uses a Z statistic to prove the hypothesis ( in contrary we must use a t - test). The z statistic is

Z = sample mean - H0 / Std Deviation sample

Z= 111-115 / 12.4 = -4/12.4 = -0.322

That's the answer of your problem

The Z  to test against your critical Z is the Z value that accumulates a 0.01 of probability or -2.32