1) A random sample of 25 employees of a local company has been measured. A 95% c

Question

1) 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.

2)A sample of 26 elements from a normally distributed population is selected. The sample mean is 10 with a standard deviation of 4. The 95% confidence interval for mu is

a. 6.000 to 14.000

b. 9.846 to 10.154

c. 8.384 to 11.616

d. 8.462 to 11.538

3) For the interval estimation of m when s is assumed known, the proper distribution to use is the

a. standard normal distribution

b. t distribution with n degrees of freedom

c. t distribution with n - 1 degrees of freedom

d. t distribution with n - 2 degrees of freedom

Explanation / Answer

1) c. 95% of the population of employees has a systolic blood pressure between 123 and 139.

2) sample mean = 10; stdev = 4

sample size n = 26

Std error = stdev/sqrt(n) = 4/sqrt(26) = 0.785

Degrees of Freedom = n - 1 = 25

Critical value for alpha 0.05 and df 25 is 2.059

Margin of Error =   Std error * Critical value = 0.785 * 2.059 = 1.616

Confidence interval = sample mean + margin of error = 10 + 1.616 = (8.384,11.616)

Ans) c. 8.384 to 11.616

3) a. standard normal distribution

We use t test when s is not known

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