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. The obtained value of the appropriate statistic for testing H 0 is _________.

Question

Quizplus · Accepted Answer

The appropriate statistic for testing the hypothesis is a one-sample t-test.

Null hypothesis: Women today weigh the same as women in previous years; μ = 115 lbs.
Alternate hypothesis: Women today weigh less than women in previous years; μ < 115 lbs.

The formula for the one-sample t-test is:
t = (x̄ - μ) / (s / √n)

where:
x̄ = sample mean = 111 lbs
μ = hypothesized population mean = 115 lbs
s = sample standard deviation = 12.4
n = sample size = 41

Substituting the values, we get:
t = (111 - 115) / (12.4 / √41) = -2.07

The obtained value of the appropriate statistic for testing H 0 is t obt = -2.07. Since the alternate hypothesis states that women today weigh less than women in previous years, we use a one-tailed test with a significance level of 0.05. The critical value of t with 40 degrees of freedom is -1.684. Since the obtained value of t obt = -2.07 is less than the critical value of t crit = -1.684, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that women today weigh less than in previous years.

A Researcher Believes That Women Today Weigh Less Than in Previous