Hypothesis Testing, P-Value and Significance Level Analysis

This assignment provides a detailed analysis of a hypothesis test concerning the proportion of female executives compared to female employees. It begins by stating the null and alternative hypotheses, followed by the calculation of the test statistic (z-score) and the p-value. The solution explains the meaning of the p-value in the context of the problem and compares it to various significance levels (0.01, 0.05, and 0.10) to determine whether to reject or fail to reject the null hypothesis. The document also explains the meaning of the test statistic and significance levels. Finally, it addresses Type I and Type II errors, with a justification for choosing a specific significance level.

Test an appropriate hypothesis with alpha 0.01, 0.05 and 0.10 and state your conclusion.
(State null and alternative hypothesis? Find the test statistic? Use P-value as your decision
criteria and state your conclusion with alpha levels 0.01, 0.05 ? and 0.10. )?
Hypothesis
H0 : p = 0.4 (female executive proportion is equal to female employees proportion)
H0 : P < 0.4 (female executive proportion is less than to female employees proportion)
Assumptions
i) Executives are independent with respect to gender
ii) the data collected is not random but a representative of the population
iii) 43 3xecutives are less than 10% of all possible executives
NP =
^p = 13
43 = 0.302
Since NP > 10%, we use z-test for this case
Test statistic
Z = ^p− p
SD ( ^p)
But
SD( ^p) = √ pq
n = √ 0.4∗0.6
43 = 0.0747
Z = 0.302−0.4
0.0747 = -1.312
Probability
P-Value = P ( ^p<0.302)

= P (z< -1.312)
= 0.0948 (From standard normal table).
Explain what the study’s P value means in this context. Did you notice the relationship with
your answer in question 1?
Since the p-value (0.0948) is greater than 0.05 at alpha =0.05, the null hypothesis is not
rejected hence we conclude that there is insufficient evidence to suggest that the female
executives proportion is less than the female employees proportion.
Since the p-value (0.0948) is greater than 0.01 at alpha =0.01, the null hypothesis is not
rejected hence we conclude that there is insufficient evidence to suggest that the female
executives proportion is less than the female employees proportion.
Since the p-value (0.0948) is less than 0.1 at alpha =0.1, the null hypothesis is rejected
hence we conclude that there is sufficient evidence to suggest that the female executives
proportion is less than the female employees proportion
Explain what the study’s test statistic means in this context.
The test statistic (z = -1.3) is less than the z critical value at alpha of 0.05 thus null hypothesis is
not rejected hence we conclude that we have insufficient evidence to suggest that female
executives proportion is less than female employees proportion.
Explain what the study’s level of significances mean in this context
Significance level means the probability of rejecting null hypothesis when it is actually true.
Which significance level would be your choice? Why? State T1 and T2 errors. ?
I choose significance level of 0.05.
Reason: Increasing significance level increases the error of rejecting null hypothesis.
Type 1 error = 0.05

Type 2 error = 1- type 1 error = 1-0.05 = 0.95