Question

Identify the null and alternative hypothesis(in symbolic and sentence form), test statistic, P-value(or critical values), conclusion about the null hypothesis, and final conclusion that addresses the original claim(Don’t just say Reject the null hypothesis or fail to reject the null hypothesis). If you used the calculator, identify everything mentioned above in addition to which calculator functions and inputs for each field were used. Test the claim that for the population of female college students, the mean weight is given by μ=132 lb Sample data are summarized as n=20, x=137lb and s=14.2. Use a significance level of α=0.10.

Answer 1

Null Hypothesis H0: The true mean weight of female college students is 132 lbs. That is, = 132

Altenative Hypothesis Ha: The true mean weight of female college students is not 132 lbs. That is,   132

Sample mean, = 137 lb

Sample standard deviation s = 14.2

Since we do not know the true population standard deviation we will conduct one sample t test.

Standard error of mean, SE = s / = 14.2 / = 3.175217

Test statistic, t = ( - ) / SE =  (137 - 132) / 3.175217 = 1.57

Degree of freedom = n-1 = 20-1 = 19

For two-tail test, p-value = 2 * p(t > 1.57, df = 19) =  0.0665

Since, p-value is less than 0.10 significance level, we reject null hypothesis H0.

There is sufficient evidence at 10% significance level to conclude that the true mean weight of female college students is not 132 lbs.