an engineer would like to design a parking garage in the most cost - effective manner. the garage must be…

an engineer would like to design a parking garage in the most cost - effective manner. the garage must be able to fit pickup trucks, which have an average height of 76.4 inches. to double - check this figure, the engineer employs a statistician. the statistician selects a random sample of 100 trucks, which will be used to determine if these data provide convincing evidence that the true mean height of all trucks is greater than 76.4 inches. the statistician plans to test the hypotheses, $h_0:mu = 76.4$ versus $h_a:mu>76.4$, where $mu$ = the true mean height of all trucks using $alpha = 0.05$. the statistician would like to increase the power of this test to reject the null hypothesis when $mu = 77$ inches. which combination of sample size and significance level would yield the greatest power of this test?\n$n = 50,alpha = 0.01$\n$n = 50,alpha = 0.10$\n$n = 200,alpha = 0.01$\n$n = 200,alpha = 0.10$

an engineer would like to design a parking garage in the most cost - effective manner. the garage must be able to fit pickup trucks, which have an average height of 76.4 inches. to double - check this figure, the engineer employs a statistician. the statistician selects a random sample of 100 trucks, which will be used to determine if these data provide convincing evidence that the true mean height of all trucks is greater than 76.4 inches. the statistician plans to test the hypotheses, $h_0:mu = 76.4$ versus $h_a:mu>76.4$, where $mu$ = the true mean height of all trucks using $alpha = 0.05$. the statistician would like to increase the power of this test to reject the null hypothesis when $mu = 77$ inches. which combination of sample size and significance level would yield the greatest power of this test?\n$n = 50,alpha = 0.01$\n$n = 50,alpha = 0.10$\n$n = 200,alpha = 0.01$\n$n = 200,alpha = 0.10$

Answer

Explanation:

Step1: Understand power - sample size and significance level relationship

The power of a hypothesis test increases with an increase in sample size ($n$) and an increase in the significance level ($\alpha$).

Step2: Analyze each option

  • For $n = 50,\alpha=0.01$: Small sample size and low significance level.
  • For $n = 50,\alpha = 0.10$: Small sample size but higher significance level compared to the first option.
  • For $n=200,\alpha = 0.01$: Large sample size but low significance level.
  • For $n = 200,\alpha=0.10$: Large sample size and high significance level.

Answer:

$n = 200,\alpha=0.10$