A company is criticized because only 16 of 40 executives at a local branch are w
ID: 3153383 • Letter: A
Question
A company is criticized because only 16 of 40 executives at a local branch are women. The company explains that although this proportion is lower than it might wish, it's not a surprising value given that only 44% of all its employees are women. The company has more than 500 executives worldwide. Test an appropriate hypothesis and state the conclusion. Determine the hypotheses for this test. (The proportion of female executives in the entire company is denoted by p.) Calculate the test statistic. Find the P-value. State the conclusion of the test. Choose the correct answer below. Because the P-value is high, fail to reject H_0. These data do not show that the proportion of women executives in the company is less than the 44% of women in the company in general. Because the P-value is high, reject H_0. These data do not show that the proportion of women executives in the company is less than the 44% of women in the company in general.Explanation / Answer
a)
Formulating the null and alternatuve hypotheses,
Ho: p = 0.44
Ha: p < 0.44 [ANSWER, D]
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b)
As we see, the hypothesized po = 0.44
Getting the point estimate of p, p^,
p^ = x / n = 0.4
Getting the standard error of p^, sp,
sp = sqrt[po (1 - po)/n] = 0.078485667
Getting the z statistic,
z = (p^ - po)/sp = -0.509647191 [ANSWER, TEST STATISTIC]
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c)
As this is a 1 tailed test, then, getting the p value,
p = 0.305149328 [ANSWER, P VALUE]
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d)
As this is a large P value, we FAIL TO REJECT THE NULL HYPOTHESIS.
OPTION A. [ANSWER]
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