A researcher believes that women today weigh less than in previous years. To investigate this belief, she randomly samples 41 adult women and records their weights. The scores have a mean of 111 lbs. and a standard deviation of 12.4. A local census taken several years ago shows the mean weight of adult women was 115 lbs. Using a = 0.01 1 tail , the critical value of the appropriate statistic for testing H ₀ is _________.

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The critical value for a one-tailed test with α = 0.01 and degrees of freedom (df) = 40 (since df = n - 1 and n = 41) is approximately -2.423. This is because the test is one-tailed and we are looking at the left tail (since the belief is that women weigh less), and the critical value corresponds to the 99th percentile of the t-distribution for 40 degrees of freedom.

A Researcher Believes That Women Today Weigh Less Than in Previous