Question

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.

bp.csv

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

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.

Answer 1

Following table shows the calculations for mean and SD of data:

	X	(X-mean)^2
	124	40.96
	128	5.76
	150	384.16
	132	2.56
	133	6.76
	152	466.56
	137	43.56
	116	207.36
	123	54.76
	126	19.36
	146	243.36
	135	21.16
	136	31.36
	132	2.56
	124	40.96
	152	466.56
	137	43.56
	107	547.56
	139	73.96
	125	29.16
	118	153.76
	128	5.76
	119	129.96
	122	70.56
	123	54.76
	111	376.36
	141	112.36
	133	6.76
	117	179.56
	146	243.36
Total	3912	4065.2

----------------------------

Conclusion: We cannot conclude that blood pressure, on average, of women in this population differs from the expected 131 mmHg.

(f)

Population should be normally distributed, And observations should be independent from other.

Since sample size is large so normality can be assumed. And it is reasonable to assume that observations are independent.