Is the mean weight of female college students still 59.4 kg? To test this,you take a random sample of 20 students,finding a mean of 61.65 kg with a standard deviation of 6.39 kg.Use a significance level of 0.10.

A) Fail to reject the null hypothesis of μ = 59.4 with a P-value of 0.1318.There is not sufficient evidence that the mean weight of female students has changed.
B) Reject the null hypothesis of μ = 59.4 with a P-value of 0.0659.There is sufficient evidence that the mean weight of female students has changed.
C) Fail to reject the null hypothesis of μ = 59.4 with a P-value of 0.9341.There is not sufficient evidence that the mean weight of female students has changed.
D) Fail to reject the null hypothesis of μ = 59.4 with a P-value of 0.8682.There is not sufficient evidence that the mean weight of female students has changed.
E) There is not enough information to perform the test.

Question

Shante Williams · Accepted Answer

Final Answer : A, Explanation :  We need to conduct a one-sample t-test since we are comparing the mean weight of the sample to the hypothesized population mean of 59.4 kg. The null and alternative hypotheses are:H0: μ = 59.4 (the mean weight of female college students is still 59.4 kg)Ha: μ ≠ 59.4 (the mean weight of female college students has changed)With a sample size of 20 and a significance level of 0.10, the degrees of freedom are 19 (df = n-1). Using a t-table or calculator, we find the t-value to be 1.734.The test statistic can be calculated as:t = (x̄ - μ) / (s / sqrt(n))t = (61.65 - 59.4) / (6.39 / sqrt(20))t = 1.369The p-value for a two-tailed test with 19 degrees of freedom is 0.1318. Since this p-value is higher than the significance level of 0.10, we fail to reject the null hypothesis. Therefore, we conclude that there is not sufficient evidence to suggest that the mean weight of female college students has changed from 59.4 kg.

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