Question

Instructions: Be sure to define all random variables, parameters, etc. Also, you must provide any code you use (final computed values are not sufficient). I strongly recommend that you create Jupyter Notebooks for this assignment, embedding your written comments in Markdown cells.

4. Systolic blood pressure was measured on 30 female diabetics between the ages of 30 and 34 from a particular ethnic group. Of interest is whether blood pressure, on average, of women in this population differs from the expected 131 mmHg. The data are available in the file bp.csv.

a. What are the null and alternative hypotheses?

b. (1 mark) What is the value of the test statistic?

c. (1 mark) What is the distribution of the test statistic if the null hypothesis is true?

d. (1 mark) What is the p-value?

e. Using a significance level of ?? = 0.05, state your conclusions in the language of the problem.

f. Name the two key unstated assumptions required for the validity of your hypothesis test and explain why they are reasonable in this context.

The data are available in the file bp.csv.

"bp" 124 128 150 132 133 152 137 116 123 126 146 135 136 132 124 152 137 107 139 125 118 128 119 122 123 111 141 133 117 146

Answer 1

a) Let denotes mean blood pressure of women between the ages of 30 and 34 from a particular ethnic group.

To test against

b) Here

sample mean

sample standard deviation

and sample size

The test statistic can be written as

which under H₀ follows a t distribution with n-1 df.

We reject H₀ at 0.05 level of significance if P-value < 0.05

Now,

The value of the test statistic

c) The distribution of the test statistic if the null hypothesis is true : t distribution with df = 30 -1 = 29

d) P-value

e) Since P-value > 0.05, so we fail to reject H₀ at 0.05 level of significance and we can conclude that there is sufficient evidence to reject the claim that blood pressure, on average, of women in this population differs from the expected 131 mmHg.

f) assumptions :

• The samples are randomly chosen from population.
• weights of the population is normally distributed.