Question

According to Gallup, 86% of incoming freshman said that getting a better job represents a critical factor in their decision to enroll in college. Consider a sample of 150 incoming freshman selected at random. Round your answers to 3 decimal places as needed.

a. Is the sampling distribution model for the sample proportion likely to be Normal? (Yes or No). Explain by stating the conditions and assumptions which must be met for the Normal model in this particular context.

b. Give the values for the mean and standard deviation of the sampling distribution model of p hat for this situation where n = 150. (Clearly write down the notations and formulas used)

Mean:                         Standard deviation:

c. Use MINITAB to create a graph of the sampling distribution model for this situation.

d. Determine the z-score associated with 134 freshman in a sample of 150 saying that getting a better job represents a critical factor in their decision to enroll in college.

i. Give the equation/formula with the values substituted.

ii. Give the value of Z.

e. Determine the probability that fewer than 123 freshmen in a sample of 150 said that getting a better job represents a critical factor in their decision to enroll in college.

f. Use MINITAB to produce the graph showing the curve with the appropriate area shaded to answer #1e. Copy and paste the graph here.

2. A survey of 845 employed people found that 31% are engaged at work. Gallup defines engaged employees as those who are involved in, enthusiastic about, and committed to their work and workplace. Round your answers to 3 decimal places as needed.

a. Use MINITAB to determine the 90% confidence interval for the proportion of employees who are engaged at work. Copy and paste the MINITAB output found in the Session window here.

b. State the formula for 90% confidence interval using appropriate notations.

c. Write the equations for the lower bound and the upper bound of the 90% confident interval with the appropriate values substituted.

Lower bound =

Upper bound =

d. Write the 90% confidence interval for proportion of people engaged at work.   

e. Interpret the meaning of this confidence interval in the context of the problem. Carefully explain what 90% confidence means in this context.

f. Determine the margin of error associated with this confidence interval.

g. What is the value of the standard error of the sample proportion?

h. Would a 95% confidence interval calculated from the same data be wider or narrower?  

Answer 1