Question

Top management of a large multinational corporation wants to create a culture of innovativeness and change. A consultant hired to assess the company’s organizational culture finds that only 15% of employees are open to new ideas and approaches toward their work. Consequently the company conducts a program for employees in order to reinforce the new corporate philosophy. Based on data collected after the program, the finds the 95% confidence interval for the proportion of all employees open to new ideas to be 18% to 22%. What should the company conclude?I. The null hypothesis should not be rejected.II. There is no evidence to suggest that the program improved employees' attitudes toward innovativeness and change.III. There is evidence that the program improved employees' attitudes toward innovativeness and change.a-III onlyb- II onlyc- Both I and IIId- Both I and IIe- I only

Answer 1

Correct option: (a) III only.

Explanation:

A (1 - α)% confidence interval can be used to make conclusion about the hypothesis test.

If the null hypothesis value is included in the interval then the null hypothesis will not be rejected. And if the null hypothesis value is not included in the interval then the null hypothesis will be rejected.

In this case it is provided that the consultant hired to assess the company’s organizational culture finds that only 15% of employees are open to new ideas and approaches toward their work.

And as a result the company conducts a program for employees in order to reinforce the new corporate philosophy.

The 95% confidence interval for the proportion of all employees open to new ideas based on the data collected is:

CI = (18%, 22%)

This 95% confidence interval for the population proportion implies that there is 95% confidence or certainty that the true proportion value is contained in the interval.

The hypothesis to test the consultant's results is:

H₀: The proportion of all employees open to new ideas is not more than 15%, i.e. p ≤ 0.15.

Hₐ: The proportion of all employees open to new ideas is more than 15%, i.e. p > 0.15.

The 95% confidence interval for the proportion of all employees open to new ideas does not contains values less than or equal to 15%.

This implies that the null hypothesis will be rejected.

Hence, concluding that the proportion of all employees open to new ideas is more than 15%.

The correct option is (a).