Question

(21 point) A company is criticized because only 13 of 43 people in executive-level positions are women. The company complains that although this proportion is lower than it might wish, it’s not a surprising value given that only 40% of all its employees are women. (a) Test an appropriate hypothesis and state your conclusion. Use α = 0.05. Be sure the appropriate assumptions and conditions are satisfied before you proceed. (Hint: conduct a one proportion z-test) Step 1: State null and alternative hypothesis. Step 2: Assumptions and conditions check, and decide to conduct a one-proportion z-test. Step 3: Compute the sample statistics and find p-value. Step 4: Interpret you p-value, compare it with α = 0.05 and make your decision. (b) Construct a 95% confidence interval for the proportion that women are in executive-level positions and interpret it. (Hint: construct a one-proportion z-interval and be sure the appropriate assumptions and conditions are satisfied before you proceed. )

Answer 1

a)

Proportion (p0) = 0.40

Total number of sample (n) = 43

number of favourable events (X) = 13

We are interested in testing the hypothesis

Since P-value of a two tailed test is equal to

P = (0.09553844867588729)

P = 0.0955

Here, the P-value is greater than the level of significance 0.05; Fail to reject the null hypothesis

Since, the test is two-tail test at \alpha = 0.05

Decision Rule: Reject the null hypothesis if the test statistic value is less than the critical value -1.6448536269514722 or greater than the critical value 1.6448536269514722

The statistic value, -1.3074 is greater than the critical values -1.6448536269514722 . Therefore, we fail to reject the null hypothesis.

b)

Sample proportion = 0.302

Sample size (n) = 43

Confidence interval(in %) = 95

z @ 95% = 1.96

Since we know that

Required confidence interval = (0.302-0.1372, 0.302+0.1372)

Required confidence interval = (0.1648, 0.4392)

With 95% confidence level we can say that the proportion that women are in executive-level positions is in between 0.165 and 0.439

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