Question

A) Which of the following statements are true?

Note that there may be more than one correct answer; select all that are true.

		As the p-value increases, the evidence against the null hypothesis also increases.
		In hypothesis testing, if the p-value is sufficiently small, then the null hypothesis can be rejected in favour of the alternate hypothesis.
		If the null hypothesis is true, then the p-value will always be greater than 0.1.
		If the null hypothesis is false, then the p-value will tend towards 0 as the sample size increases.
		The validity of the results from hypothesis testing is dependent upon the use of simple random samples and further assumptions involving sample size or normality of the population.

B) Test the null hypothesis H0:p=0.5against the alternative hypothesis HA:p<0.5, when 95 individuals in a random sample of 217 have a characteristic of interest.

Calculate the value of the z test statistic, for testing the null hypothesis that the population proportion is 0.5. Round your response to at least 2 decimal places.

The P-value falls within which one of the following ranges:

A		P-value > 0.50
B		0.10 < P-value < 0.50
C		0.05 < P-value < 0.10
D		P-value < 0.05

What conclusion can be made, at the 5% level of significance?

A		There is sufficient evidence to reject the null hypothesis, in favour of the alternative that the population proportion is less than 0.5.
B		There is insufficient evidence to reject the null hypothesis, and therefore no significant evidence that the population proportion is not 0.5.

C) Test the null hypothesis H0:p=0.8against the alternative hypothesis HA:p>0.8, when 806 individuals in a random sample of 1,002 have a characteristic of interest.

a) Calculate the value of the z test statistic, for testing the null hypothesis that the population proportion is 0.8. Round your response to at least 2 decimal places.

b) Find the corresponding P-value for the above test statistic.Round your response to at least 4 decimal places.

c) What conclusion can be made, at the 10% level of significance?

A		There is sufficient evidence to reject the null hypothesis, in favour of the alternative that the population proportion is greater than 0.8.
B		There is insufficient evidence to reject the null hypothesis, and therefore no significant evidence that the population proportion is not 0.8.

D) Suppose a random sample of size 9 is taken from a normally distributed population, and the sample mean and variance are calculated to be x¯=47.2 and s2=4.5respectively.

Use this information to test the null hypothesis H0:μ=50versus the alternative hypothesis HA:μ≠50, at the 5% level of significance.

a) What is the value of the test statistic t, for testing the null hypothesis that the population mean is equal to 50? Round your response to at least 2 decimal places.

b) The P-value falls within which one of the following ranges:

A		P-value > 0.10
B		0.05 < P-value < 0.10
C		0.025 < P-value < 0.05
D		0.01 < P-value < 0.025
E		P-value < 0.01

c) Is the null hypothesis rejected at the 5% level of significance? Yes or No

Answer 1

(A) Correct Answers: (ii), (iii) and (iv)

> Option (ii): In hypothesis testing, if the p-value is sufficiently small, then the null hypothesis can be rejected in favour of the alternate hypothesis.

> Option (iii): If the null hypothesis is false, then the p-value will tend towards 0 as the sample size increases.

> Option (iv): The validity of the results from hypothesis testing is dependent upon the use of simple random samples and further assumptions involving sample size or normality of the population.

* Conclusion: Option (A): There is sufficient evidence to reject the null hypothesis, in favour of the alternative that the population proportion is less than 0.5.

(c) Option (A): There is sufficient evidence to reject the null hypothesis, in favour of the alternative that the population proportion is greater than 0.8.