Question

Can i please get detailed answer for this question from my assignment. it has overall weightage of 9 marks. Thanks

We are interested in estimating the mean systolic blood pressure for female diabetics between the ages of 30 and 34. For the purposes of this question you may assume that blood pressure in this population has a normal distribution with standard deviation of 11.8 mmHg.

a. A random sample of 10 women is selected from this population. The average systolic blood pressure in this sample is 130 mmHg. Calculate (by hand) a 95% confidence interval ,the mean systolic blood pressure in the population of female diabetics aged 30 to 34.

b. Interpret your confidence interval in a) in words. (What does “95% confidence” mean?)

c. Is your confidence interval in a) exact or approximate? Explain.

d. How large would the random sample of women need to be for a 99% confidence interval to have a total width of 10 mmHg?

Answer 1

a) For 95% confidence loevel, critical value of z is . The 95% confidence interval ,the mean systolic blood pressure in the population of female diabetics aged 30 to 34 is:

b) We are 95% confident that true mean systolic blood pressure in the population of female diabetics aged 30 to 34 lies between 122.69 and 137.31.

95% confidence means if we take many samples of size 10 from same population, we expect 95% of the confidence intervals will contain true mean systolic blood pressure.

c) No because we expect that there are 5% confidence intervals do not contain true mean and this interval can be one of them.

d) Margin of error, E = width/2 = 10/2 = 5

For 99% confidence loevel, critical value of z is .

The sample size is: