Question

A ski resort tracks the proportion of seasonal employees who are rehired each season. Rehiring a seasonal employee is beneficial in many ways, including lowering the costs incurred during the hiring process such as training costs. A random sample of 859 full-time and 385 part-time seasonal employees from 2009 showed that 457 full-time employees were rehired compared with 186 part-time employees. (a) Is there a significant difference in the proportion of rehires between the full-time and part-time seasonal employees? (Use $\alpha = 0.10$.) (a-1) Choose the appropriate hypotheses. Assume $\pi_f$ is the proportion of full-time employees and $\pi_p$ is the proportion of part-time employees. $H_0: \pi_f - \pi_p = 0$ vs. $H_1: \pi_f - \pi_p \ne 0$ $H_0: \pi_f - \pi_p \ge 0$ vs. $H_1: \pi_f - \pi_p < 0$ $H_0: \pi_f - \pi_p \le 0$ vs. $H_1: \pi_f - \pi_p > 0$ (a-2) Specify the decision rule. (A negative value should be indicated by a minus sign. Round your answers to 3 decimal places.) Reject the null hypothesis if $z_{calc} >$ 1.645 or $z_{calc} <$ -1.645 (a-3) Find the test statistic $z_{calc}$. (Round intermediate calculations to 4 decimal places. Round your answer to 3 decimal places.) $z_{calc}$ 1.019 (a-4) Make a decision. We do not reject the null hypothesis. (a-5) Make a decision. We cannot conclude that there is a significant difference in the proportion of rehires between the full-time and part-time seasonal employees. (b) Find the p-value. (Round your answer to 4 decimal places.) p-value 0.3082

          A ski resort tracks the proportion of seasonal employees who are rehired each season. Rehiring a seasonal employee is beneficial in many ways, including lowering the costs incurred during the hiring process such as training costs. A random sample of 859 full-time and 385 part-time seasonal employees from 2009 showed that 457 full-time employees were rehired compared with 186 part-time employees.
(a) Is there a significant difference in the proportion of rehires between the full-time and part-time seasonal employees? (Use $\alpha = 0.10$.)
(a-1) Choose the appropriate hypotheses. Assume $\pi_f$ is the proportion of full-time employees and $\pi_p$ is the proportion of part-time employees.
$H_0: \pi_f - \pi_p = 0$ vs. $H_1: \pi_f - \pi_p \ne 0$
$H_0: \pi_f - \pi_p \ge 0$ vs. $H_1: \pi_f - \pi_p < 0$
$H_0: \pi_f - \pi_p \le 0$ vs. $H_1: \pi_f - \pi_p > 0$
(a-2) Specify the decision rule. (A negative value should be indicated by a minus sign. Round your answers to 3 decimal places.)
Reject the null hypothesis if $z_{calc} >$ 1.645 or $z_{calc} <$ -1.645
(a-3) Find the test statistic $z_{calc}$. (Round intermediate calculations to 4 decimal places. Round your answer to 3 decimal places.)
$z_{calc}$ 1.019
(a-4) Make a decision.
We do not reject the null hypothesis.
(a-5) Make a decision.
We cannot conclude that there is a significant difference in the proportion of rehires between the full-time and part-time seasonal employees.
(b) Find the p-value. (Round your answer to 4 decimal places.)
p-value 0.3082

A ski resort tracks the proportion of seasonal employees who are rehired each season. Rehiring a seasonal employee is beneficial in many ways, including lowering the costs incurred during the hiring process such as training costs. A random sample of 859 full-time and 385 part-time seasonal employees from 2009 showed that 457 full-time employees were rehired compared with 186 part-time employees.
(a) Is there a significant difference in the proportion of rehires between the full-time and part-time seasonal employees? (Use α = 0.10.)
(a-1) Choose the appropriate hypotheses. Assume is the proportion of full-time employees and is the proportion of part-time employees.
H0: - = 0 vs. H1: - 0
H0: - ≥ 0 vs. H1: - < 0
H0: - ≤ 0 vs. H1: - > 0
(a-2) Specify the decision rule. (A negative value should be indicated by a minus sign. Round your answers to 3 decimal places.)
Reject the null hypothesis if zcalc > 1.645 or zcalc < -1.645
(a-3) Find the test statistic zcalc. (Round intermediate calculations to 4 decimal places. Round your answer to 3 decimal places.)
zcalc 1.019
(a-4) Make a decision.
We do not reject the null hypothesis.
(a-5) Make a decision.
We cannot conclude that there is a significant difference in the proportion of rehires between the full-time and part-time seasonal employees.
(b) Find the p-value. (Round your answer to 4 decimal places.)
p-value 0.3082

Added by Amanda H.

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