TRUE/FALSE: Hypothesis Testing Please answer ‘True in all cases’ or ‘False for a
ID: 3291816 • Letter: T
Question
TRUE/FALSE: Hypothesis Testing
Please answer ‘True in all cases’ or ‘False for at least one case’. Briefly justify your answers.
(a) One minus the p-value is the probability that the alternative hypothesis is true.
(b) The further the hypothesized mean is from the actual mean the greater the power of the test.
(c) The larger the p-value, the more we doubt the null hypothesis.
(d) Suppose X and Y are uncorrelated. Then X and Y are independent.
(e) A Type II error is failing to reject a false null hypothesis.
(f) You cannot make a Type II error when the null hypothesis is true.
(g) If the null hypothesis is rejected, it is concluded that the alternative hypothesis is true.
(h) If the null hypothesis is not rejected, we conclude that the null hypothesis is true.
(i) If a null hypothesis is rejected at a significance level of .05, it will always be rejected at a significance level of .01
(j) If a one-sided null hypothesis is rejected at a given significance level, then the corresponding two-sided null hypothesis (i.e., the same sample size, the same standard deviation, and the same mean) will always be rejected at the same significance level.
(k) Let X1, ..., Xn N(µ, 2 ) (n large), H0 : µ = µ0, H1 : µ 6= µ0 and suppose you conduct a hypothesis test and you fail to reject the null hypothesis. If you calculate the corresponding confidence interval, µ0 will be the center of the interval.
Explanation / Answer
Dear student,
According to Chegg guidelines only first four are answered.
a, True. Since higher the p value , higher is a chance of the null hypothesis to be acepted.
b,True. Since the increase in interval increases the chances of H0 to be rejected. Thus, the power of the test increases.
c,False. Since higher the p value , higher is a chance of the null hypothesis to be acepted.
d,False. Though the inverse is true. but the uncollinearity do not imple independence.
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