(a) Consider testing H0: μ1-μ2=-1.0 versus Ha: μ1-μ2<-1.0 at level 0.01 . Describe in words what

For part A, I'll note that our alternate hypothesis, mu1 -mu2, is less than negative 1. We can w

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(a) Consider testing \( H_{0}: \mu_{1}-\mu_{2}=-1.0 \) versus \( H_{a}: \mu_{1}-\mu_{2}<-1.0 \) at level 0.01 . Describe in words what \( H_{a} \) says, and then carry out the test. - \( H_{a} \) says that the average heat output for sufferers is more than \( 1 \mathrm{cal} / \mathrm{cm}^{2} / \mathrm{min} \) below that of non-sufferers. \( H_{a} \) says that the average heat output for sufferers is the same as that of non-sufferers. \( H_{a} \) says that the average heat output for sufferers is less than \( 1 \mathrm{cal} / \mathrm{cm}^{2} / \mathrm{min} \) below that of non-sufferers Calculate the test statistic and \( P \)-value. (Round your test statistic to two decimal places and your \( P \)-value to four decimal places.) \( \begin{array}{rrr}z & = \\ P-\text { value } & = & x\end{array} \) State the conclusion in the problem context. Fail to reject \( H_{0} \). The data suggests that the average heat output for sufferers is less than \( 1 \mathrm{cal} / \mathrm{cm}^{2} / \mathrm{min} \) below that of non-sufferers. Fail to reject \( H_{0} \). The data suggests that the average heat output for sufferers is the same as that of non-sufferers. Reject \( H_{0} \). The data suggests that the average heat output for sufferers is the same as that of non-sufferers. (b) What is the probability of a type II error when the actual difference between \( \mu_{1} \) and \( \mu_{2} \) is \( \mu_{1}-\mu_{2}=-1.3 \) ? (Round your answer to four decimal places.) ) (c) Assuming that \( m=n \), what sample sizes are required to ensure that \( \beta=0.1 \) when \( \mu_{1}-\mu_{2}=-1.3 \) ? (Round your answer up to the nearest whole number.) subjects

          (a) Consider testing \( H_{0}: \mu_{1}-\mu_{2}=-1.0 \) versus \( H_{a}: \mu_{1}-\mu_{2}<-1.0 \) at level 0.01 . Describe in words what \( H_{a} \) says, and then carry out the test.
- \( H_{a} \) says that the average heat output for sufferers is more than \( 1 \mathrm{cal} / \mathrm{cm}^{2} / \mathrm{min} \) below that of non-sufferers.
\( H_{a} \) says that the average heat output for sufferers is the same as that of non-sufferers.
\( H_{a} \) says that the average heat output for sufferers is less than \( 1 \mathrm{cal} / \mathrm{cm}^{2} / \mathrm{min} \) below that of non-sufferers
Calculate the test statistic and \( P \)-value. (Round your test statistic to two decimal places and your \( P \)-value to four decimal places.)
\( \begin{array}{rrr}z & = \\ P-\text { value } & = & x\end{array} \)
State the conclusion in the problem context.
Fail to reject \( H_{0} \). The data suggests that the average heat output for sufferers is less than \( 1 \mathrm{cal} / \mathrm{cm}^{2} / \mathrm{min} \) below that of non-sufferers.
Fail to reject \( H_{0} \). The data suggests that the average heat output for sufferers is the same as that of non-sufferers.
Reject \( H_{0} \). The data suggests that the average heat output for sufferers is the same as that of non-sufferers.
(b) What is the probability of a type II error when the actual difference between \( \mu_{1} \) and \( \mu_{2} \) is \( \mu_{1}-\mu_{2}=-1.3 \) ? (Round your answer to four decimal places.) )
(c) Assuming that \( m=n \), what sample sizes are required to ensure that \( \beta=0.1 \) when \( \mu_{1}-\mu_{2}=-1.3 \) ? (Round your answer up to the nearest whole number.) subjects

(a) Consider testing H0: μ1-μ2=-1.0 versus Ha: μ1-μ2<-1.0 at level 0.01 . Describe in words what Ha says, and then carry out the test.
- Ha says that the average heat output for sufferers is more than 1 cal / cm^2 / min below that of non-sufferers.
Ha says that the average heat output for sufferers is the same as that of non-sufferers.
Ha says that the average heat output for sufferers is less than 1 cal / cm^2 / min below that of non-sufferers
Calculate the test statistic and P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)
z =
P- value = x
State the conclusion in the problem context.
Fail to reject H0. The data suggests that the average heat output for sufferers is less than 1 cal / cm^2 / min below that of non-sufferers.
Fail to reject H0. The data suggests that the average heat output for sufferers is the same as that of non-sufferers.
Reject H0. The data suggests that the average heat output for sufferers is the same as that of non-sufferers.
(b) What is the probability of a type II error when the actual difference between μ1 and μ2 is μ1-μ2=-1.3 ? (Round your answer to four decimal places.) )
(c) Assuming that m=n, what sample sizes are required to ensure that β=0.1 when μ1-μ2=-1.3 ? (Round your answer up to the nearest whole number.) subjects

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