Please please Save me 1 Please circle T or F based on whethe

Please please Save me!

1. Please circle T or F based on whether the following statements are True or False respectively.

a) T F A 95% confidence interval will be larger than a 99% CI

b) T F A 99% CI will capture the population parameter 99% times

c) T F For large sample the sample mean is approximately normal

d) T F The center of a confidence interval for (\'mu\' greek word) is (mean)

e) T F Confidence interval can be used to test one tailed hypothesis

f) T F Type-I error is the probability to reject (H0) ! when it is true

g) T F p-value can be greater than 1

h) T F Central limit theorem (CLT) gives the distribution of sample mean

2. The UNO human resources department wanted to know about the average student employee wage rate of Omaha area. They randomly selected 30 student employees and recorded their wage rates. The sample mean and standard deviation of the wage rates are obtained as $10.2 and $3.1 respectively. Using 68-95-99.7 rule of normal distribution please answer the following questions.

a) Compute the 95% Confidence Interval (CI) for true mean wage rate (\'mu\' greek letter).

b) Interpret the confidence interval you just computed.

c) Compute the 99.7% confidence interval for true mean wage rate (mu letter)

d) For which confidence level, do you think the range (width) of interval is larger?

I) 95% CI II) 99.7% CI

e) Suppose, we construct a 75% confidence interval of true mean wage rate (mu). What do you think about the width of 75% confidence Interval (CI) compared to the width of the 95% confidence interval? I) Larger than 95% II) Smaller than 95%

f) Now if they would have selected 25 students and obtained the same mean and standard deviation of wage rate, what would be the 95% Confidence Interval (CI) for true mean wage rate (mu).

g) Is the confidence interval in a) larger than what we have in f)? Why or why not?

h) Suppose new sample standard deviation is $2.5, when 25 students were selected and mean remains the same. . What would be the 95% CI?

i) Is the confidence interval in f) larger than what we have in h)? Why or why not?

Solution

1. Please circle T or F based on whether the following statements are True or False respectively.
a) T F A 95% confidence interval will be larger than a 99% CI
False, Higher the interval larger the width

b) T F A 99% CI will capture the population parameter 99% times
False, We claim that we are 99% confident that true mean lies in the interval we achived

c) T F For large sample the sample mean is approximately normal
True, When sample size greater han 30, we assme it is normal

d) T F The center of a confidence interval for (\'mu\' greek word) is (mean)
True, interval achived is increased or decreased margin of error from Mean

e) T F Confidence interval can be used to test one tailed hypothesis
True, we can , until requested

f) T F Type-I error is the probability to reject (H0) ! when it is true
True, It is Reject Ho, when Ho is True