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Answer :
The given problem is concerned with hypothesis testing. The 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 obtained value of the appropriate statistic for testing H0 is t= -2.42.
Given that,
Population mean µ = 115 lbs
Sample mean x = 111 lbs
Sample size n = 41
Standard deviation σ = 12.4 lbs
hypothesis testing
Null hypothesis H0: µ = 115 lbs
Alternate hypothesis H1: µ < 115 lbs
Since the population standard deviation is unknown and the sample size is less than 30, we use a t-distribution to test the hypothesis. The formula for the t-test statistic is,
t= (x- µ)/(s/√n)
Where, x = sample mean, µ = population mean, s = sample standard deviation, and n = sample size
Substituting the given values in the above formula, we get,
t= (111 - 115) / (12.4/ √41)t= -4 / 1.93t= -2.07
The obtained value of the appropriate statistic for testing H0 is t= -2.07.
The calculated t-value is compared with the critical value of t with degrees of freedom (df) = n-1 = 41-1 = 40 at the desired significance level. If the calculated t-value is less than the critical value of t, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
You can learn more about the hypothesis at: brainly.com/question/32562440
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