Question

1. A random sample of 29 BSN nurses at a large Michigan hospital have the average (mean) hourly wage of $37.55 with the standard deviation of $4.66. If we want a 99% confidence interval to have a margin of error of no more than $3, what is the minimum required sample size we should take? (Hint: use t*=2.7633)

2. A test of the hypotheses H0: mu=17 vs. Ha: mu >17 is conducted. Sample data of n=30 cases provides x-bar=14 with s=6. Compute the estimate of the effect size in this case. Round your answer to 1 decimal place.

3. In Q4 the estimate of the effect size was found to be -0.5. Interpret this estimate.

A) This result suggests that the true mean is 0.5 standard deviations below the mean hypothesized by the null model

B) This result suggests that the true mean is 0.5 standard deviations above the mean hypothesized by the null model

4. A Type I Error occurs when

A) we decide in favor of Ha when H0 is true

B) we decide in favor of Ha when H0 is false

5. A power of a test is

A) the probability of rejecting H0 when H0 is true

B) the probability of rejecting H0 when H0 is false

C) the probability of rejecting Ha when Ha is true

D) the probability of rejecting Ha when Ha is false

Answer 1

1. A random sample of 29 BSN nurses at a large Michigan hospital have the average (mean) hourly wage of $37.55 with the standard deviation of $4.66. If we want a 99% confidence interval to have a margin of error of no more than $3, what is the minimum required sample size we should take? (Hint: use t*=2.7633)?

Answer)

Margin of error (MOE) = t*s.d/√n

t = 2.7633

We need to find n

S.d = 4.66

MOE = 3

3 = 2.7633*4.66/√n

N = 19

2. A test of the hypotheses H0: mu=17 vs. Ha: mu >17 is conducted. Sample data of n=30 cases provides x-bar=14 with s=6. Compute the estimate of the effect size in this case. Round your answer to 1 decimal place.

Effect size = (sample mean - claimed mean)/s.d

= (14 - 17)/6

= -0.5