A random sample of 25 employees of a local company has been measured. A 95% conf

Question

A random sample of 25 employees of a local company has been measured. A 95% confidence interval estimate for the mean systolic blood pressure for all company employees is 123 to 139. Which of the following statements is valid?

a) 95% of the sample of employees has a systolic blood pressure between 123 and 139.
b) If the sampling procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure.
c) 95% of the population of employees has a systolic blood pressure between 123 and 139.
d) If the sampling procedure were repeated many times, 95% of the sample means would be between 123 and 139.





A random sample of 25 observations was taken from a normally distributed population. The average in the sample was 84.6 with a variance of 400. Construct a 90% confidence interval for m.
a) 77.756 to 91.444
b) 73.412 to 95.788
c) 78.021 to 91.179
d) 79.474 to 89.726

Explanation / Answer

For the first question the answer is d, because a 95% confidence interval means the true value will be captured by the confidence interval 95% of the time.

For the second question you can use a TI-83 or 84 to easily answer this question. Select STAT then TESTS and choose 8: TINTERVAL. Select Stats as the input method. First you have to calculate standard deviation from the given value for variance. Standard deviation is the square root of variance. Therefore the standard deviation is the square root of 400, which is 20. Then input the given statistics and select calculate. You should get (77.756, 91.444), so a is your answer.

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