We take a random sample of n individuals and measure the value of some variable

Question

We take a random sample of n individuals and measure the value of some variable X. We conduct a hypothesis test of H0: ? = 100 vs. Ha: ? > 100 at the 5% level of significance. We calculate a sample mean of x??? x ¯ = 105 and we reject the null hypothesis. Using the same data, assess if each of the statements in Questions 11 to 13 must be true or is not necessarily true.

Question 11 Unsaved A test of H0: ? = 100 vs. Ha: ? > 100 at the 10% level of significance would also result in the rejection of H0.

Question 11 options:

A) Must be true

B) Not necessarily

Question 12 Unsaved A test of H0: ? = 101 vs. Ha: ? > 101 at the 5% level of significance would also result in the rejection of H0.

Question 12 options:

A) Must be true

B) Not necessarily

Question 13 Unsaved A test of H0: ? = 100 vs. Ha: ? ? 100 at the 5% level of significance would also result in the rejection of H0. Question 13 options:

A) Must be true

B) Not necessarily

Explanation / Answer

#11.
Must be true (option A)
Because the p-value < 0.05 as rejection happens for 5% significance level.
p-value will be less than 0.1 i.e. 10%

#12.
Not necessarily (option B)
here hypothesised mean is changed to 101 which will result into the change in test statistic and hence p-value.
This may change the decision.

#13.
Please provide the correct alternate hypothesis. there are 2 question marks in the question.

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