Question

Suppose that there is a very small p-value in the row labeled “treatments” in the ANOVA table for a completely randomized design. True or False: This suggests that all the treatment levels have the same true mean

) For simple linear regression, suppose that we examine a residual plot and find that the residuals are generally more-dispersed at lower levels of the explanatory variable. True or False: This suggests that one of the assumptions for simple linear regression is violated.

) Suppose we compute a two-sided 99% t-interval for the mean µ, and we find that 30.0 does not lie inside the interval. Consider a t-test of H0 : µ = 30.0 versus HA : µ 6= 30.0 True or False: From this information, we can determine whether or not the t-test rejects H0 at significance level α = 0.04.

True or False: In a hypothesis test, the p-value is a quantity that is chosen by the person who performs the hypothesis test.

Answer 1

Statement: This suggests that one of the assumptions for simple linear regression is violated.

Answer: true, because it is assumed in simple linear regression that residuals follow normal distribution. Hence the residual plot must be symmetrical.

Statement: From this information, we can determine whether or not the t-test rejects H0 at significance level α = 0.04.

Answer: true, because if value lie outside the 99% confidence interval this means that p value is less than 0.01 which is less than 0.4. Since p value is less than 0.4 hence it is determined that h0 mist be rejected.

Statement: True or False: In a hypothesis test, the p-value is a quantity that is chosen by the person who performs the hypothesis test.

Answer: false because p value is calculated mathematically using statistical tables.