Hypothesis testing need answer please

Question

An engineering company wants to have a hypothesis test on its certain type of products. A quality control engineer measures the strength of 16 sample products of that type, and computes a sample mean equal to 103.7 and sample variance equal to 36.

1. Perform a hypothesis test at significance level equal to 0.05 and analyze the claim that the average strength of this type of products is less than 108.

2. Perform a hypothesis test at significance level equal to 0.05 and analyze the claim that the variance of this type of products is not equal to 28.

Answer 1

1.

Ho: mu = 108

Ha: mu < 108

Compute t = (sample mean - mu)/(standard deviation/square root(sample size))

compute P(t < computed t) for 15 DOF. If < 0.05, then reject Ho.

alternatively determine critical left-sided t for 15 DOF and alpha = 0.05. If t < t-critical value, then reject Ho.

2.

Ho: variance = 28

Ha: variance != 28

compute chi-square = (sample size - 1) * sample variance / population variance

if computed chi-square > tabled chi-square for 0.025 and 15 or computed chi-square < tabled chi-square for 0.975 and 15, then reject Ho.