A group of local businesspersons is interested is finding out how long newly hir

Question

A group of local businesspersons is interested is finding out how long newly hired UTEP business graduates remain in their first jobs. The group wants to estimate the population mean time on the first job with 95% confidence. A random sample of subjects was taken: Number of Years on First Job 3, 4, 7, 1, 12, 1, 2, 2, 5 4, 2, 3, 1, 3, 4, 2, 6, 7 You know that the confidence interval estimate of the population mean for this sample is: U = X bar +/- t S_X bar where u = population mean Or Upper Limit = X bar + t S_X bar X bar = sample mean Lower Limit = X bar - t S_X bar t = Critical value of t @ 95% S_X bar = Standard Error of the Mean S = Sample Standard Deviation n = sample size The following steps are required to answer the research question: a. Calculate the sample mean, X bar b. Estimate the population standard deviation by calculating S the sample standard deviation. S = squareroot elementof^18 _ (X_ - X bar)/(n - 1) = c. Estimate the Standard Error of the Mean (S_X bar) d. Is the hypothesis or research question one or two tailed? e. Calculate the degrees of freedom f. Determine the critical t-values associated with the 95% confidence level from the t Distribution table. g. Given the above, what is the t distribution critical value? h. Calculate the lower and upper limits of the confidence interval. i. What is the confidence interval @ 95% for the mean number of years spent on the first job? J. If the group had estimated the mean number of years spend on the first job to be two (2) years, would the hypothesis be accepted or rejected. Explain your answer.

Explanation / Answer

Question a

From the given data, we have

Sample mean = Xbar = 3.833333

Question b

From the given data, we have

Sample standard deviation = S = 2.791795

Question c

The formula for standard error is given as below:

Standard error = standard deviation / sqrt(n)

We are given

Sample size = n = 18

Sample standard deviation = S = 2.791795

Standard error = 2.791795/sqrt(18) = 0.658032

Standard error =0.658032

Question d

The hypothesis or research question is two tailed.

Question e

Degrees of freedom = n – 1 = 18 – 1 = 17

Degrees of freedom = 17

Question f

We are given

Confidence level = 95%

Degrees of freedom = 17

So, critical t values = 2.1098 and -2.1098

Question g

The t distribution critical value is 2.1098.

Question h

The confidence interval formula is given as below:

Confidence interval = Xbar -/+ t*Standard error

Lower limit = Xbar – t*Standard error

Lower limit = 2.7917947 - 2.1098* 0.658032321

Lower limit = 2.4450

Upper limit = Xbar + t*Standard error

Upper limit = 2.7917947 + 2.1098* 0.658032321

Upper limit = 5.2217

Question i

Confidence interval = (2.4450, 5.2217)

We are 95% confident that the mean number of year spent on the first job will be lies between 2.4450 years and 5.2217 years.

Question j

The value 2 years is not included in the given confidence interval, so hypothesis would be rejected.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.