please explain these,

1) The heights of 82 roller coasters have a mean of 280.7 feet and a population standard deviation of 59.3 feet. Find the standardized tests statistics and the corresponding p-value when the claim is that roller coasters are more than 290 feet tall

z-test statistic = -1.42, p-value = 0.1556

z-test statistic = -1.42, p-value = 0.0778

z-test statistic = 1.42, p-value = 0.1556

z-test statistic = 1.42, p-value = 0.0778

2) A travel analyst claims that the mean room rates at a three-star hotel in Chicago is greater than $152. In a random sample of 36 three-star hotel rooms in Chicago, the mean room rate is $163 with a population standard deviation of $41. At =0.10, what type of test is this and can you support the analyst's claim using the p-value?

Claim is the alternative, reject the null as p-value (0.054) is less than alpha (0.10), and can support the claim

Claim is the null, reject the null as p-value (0.054) is less than alpha (0.10), and cannot support the claim

Claim is the null, fail to reject the null as p-value (0.054) is less than alpha (0.10), and cannot support the claim

Claim is the alternative, fail to reject the null as p-value (0.054) is less than alpha (0.10), and can support the claim

3) A car company claims that the mean gas mileage for its luxury sedan is at least 24 miles per gallon. A random sample of 7 cars has a mean gas mileage of 23 miles per gallon and a standard deviation of 3.5 miles per gallon. At =0.05, can you support the company's claim assuming the population is normally distributed?

Yes, since the test statistic is not in the rejection region defined by the critical value, the null is not rejected. The claim is the null, so is supported

Yes, since the test statistic is not in the rejection region defined by the critical value, the null is not rejected. The claim is the null, so is supported

No, since the test statistic is in the rejection region defined by the critical value, the null is rejected. The claim is the null, so is not supported

No, since the test statistic is not in the rejection region defined by the critical value, the null is not rejected. The claim is the null, so is supported