A college student is doing some research on the cost of one-bedroom apartments i

Question

A college student is doing some research on the cost of one-bedroom apartments in town. He has randomly selected 25 apartments for which the price was published. The average price for these apartments is = $652. He will assume that price follows roughly a Normal distribution. Based on prices from previous years, a real estate agent gives him the information that is approximately $55. A 95% confidence interval for is found to be 652 ± 21.56 = ($630.44, $673.56). Determine which of the following statements is TRUE.

A test of the hypotheses H0: = 650 versus Ha: 650 would be rejected at the 0.05 level. A test of the hypotheses H0: = 650 versus Ha: > 650 would be rejected at the 0.05 level. A test of the hypotheses H0: = 675 versus Ha: 675 would be rejected at the 0.05 level. All of the above

Explanation / Answer

Since 650 lies in the confidence interval range, we can't reject the null hypothesis Ho: = 650 at 0.05 level so option 1 and option 2 got eliminated.

Now, we can see that 675 lies outside the 95% confidence interval and hence,

A test of the hypotheses H0: = 675 versus Ha: 675 would be rejected at the 0.05 level.

Option C is correct.

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