Perform a significance test, using the normal distribution as prescribed by the

Question

Perform a significance test, using the normal distribution as prescribed by the CLT. Write your hypotheses, find your P-value (which will be only an approximation), and write both the analytical conclusion and the public statement.

35. Women executives A company is only because only 13 of 43 people in because women. executive-level are The company explains 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. What do you think? Test an appropriate hypothesis and state your conclusion. Be sure the appropriate assumptions and con- ditions are satisfied before you proceed.

Explanation / Answer

Population proportion, p = 0.4

Sample proportion, p' = 13/43 = 0.302

Sample size, n = 43

SE of sample propotion, SEp' = ( (p(1-p)) /n)0.5 = ( (0.4(1-0.4)) /43)0.5 =0.074

Test statistic, z = (p'-p)/SEp' = (0.302-0.4)/0.074 = -1.324

Hypothesis are:

H0 : p' = 0.4

Ha : p' < 0.4

Assuming a significance level of 5%, the critical z-score for a left tailed test at this significane level is:

zc = -1.64

Since z lies within the acceptance region, so null hypothesis can't be rejected.

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