Question

A survey of business and IT executives found that 76​% of automotive​ executives, 66​% of financial services​ executives, 81​% of heath care​ executives, 57​% of retail​ & consumer​ executives, and 75​% of technology executives say their CEOs are active champions of using digital technology to achieve strategy. Suppose that the study was based on a sample size of 500 in each group. Complete parts​ (a) and​ (b).

a. At the 0.05 level of​ significance, is there evidence of a difference among the industries with respect to the proportion of executives that say their CEOs are active champions of using digital technology to achieve​ the strategy?

State the null and alternative hypotheses

The test statistic is chi Subscript STAT Superscript 2χ2STATequals=

The critical value for alpha equals 0.05 is

b. Compute the​ p-value and interpret its meaning.

P-VALUE:

What does the​ p-value mean?

A.The​ p-value is the probability that the null hypothesis is true.

B. The​ p-value is the probability of falsely rejecting the null hypothesis.

C.The​ p-value is the probability of rejecting the null hypothesis if the test were repeated for different samples

D. The​ p-value is the probability of obtaining a result at least as extreme as the one obtained with this sample given that the null hypothesis is true.

Answer 1

a.)

Null Hypothesis (H0) : There is not any significant difference among the industries with respect to the proportion of executives.

Alternative Hypothesis (H1) : There is a significant difference among the industries with respect to the proportion of executives.

Test statistic is 3.516141.

b)

p-value is 9.487729 at 5% level of significance and p-value is the probabiltity of obtaining a result at least as extreme as the one obtained with this sample given that the null hypothesis is true.