Question

An avid traveler is investigating whether travel websites differ in their pricing. She chooses a random sample of 32 hotel rooms from across the state and notes the price of each room from site A and site B. The mean difference (site A – site B) in the prices for the rooms is $5.49 with a standard deviation of $18.65. Assuming the conditions for inference have been met, is there evidence that the prices of hotel rooms from site A and site B are different, on average? Use a significance level of α = 0.05. Because the P-value is less than α, there is evidence that the prices of hotel rooms from site A and site B are different, on average. Because the P-value is greater than α, there is evidence that the prices of hotel rooms from site A and site B are different, on average. Because the P-value is less than α, there is not sufficient evidence that the prices of hotel rooms from site A and site B are different, on average. Because the P-value is greater than α, there is not sufficient evidence that the prices of hotel rooms from site A and site B are different, on average.

          An avid traveler is investigating whether travel websites differ in their pricing. She chooses a random sample of 32 hotel rooms from across the state and notes the price of each room from site A and site B. The mean difference (site A – site B) in the prices for the rooms is $5.49 with a standard deviation of $18.65. Assuming the conditions for inference have been met, is there evidence that the prices of hotel rooms from site A and site B are different, on average? Use a significance level of α = 0.05.

Because the P-value is less than α, there is evidence that the prices of hotel rooms from site A and site B are different, on average.
Because the P-value is greater than α, there is evidence that the prices of hotel rooms from site A and site B are different, on average.
Because the P-value is less than α, there is not sufficient evidence that the prices of hotel rooms from site A and site B are different, on average.
Because the P-value is greater than α, there is not sufficient evidence that the prices of hotel rooms from site A and site B are different, on average.

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Added by Paul E.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Frank Deng

08/29/2022

Step 1

H0: The mean difference in prices between site A and site B is zero (i.e., there is no difference in prices). H1: The mean difference in prices between site A and site B is not zero (i.e., there is a difference in prices). Show more…

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An avid traveler is investigating whether travel websites differ in their pricing. She chooses a random sample of 32 hotel rooms from across the state and notes the price of each room from site A and site B. The mean difference (site A – site B) in the prices for the rooms is $5.49 with a standard deviation of $18.65. Assuming the conditions for inference have been met, is there evidence that the prices of hotel rooms from site A and site B are different, on average? Use a significance level of α = 0.05. Because the P-value is less than α, there is evidence that the prices of hotel rooms from site A and site B are different, on average. Because the P-value is greater than α, there is evidence that the prices of hotel rooms from site A and site B are different, on average. Because the P-value is less than α, there is not sufficient evidence that the prices of hotel rooms from site A and site B are different, on average. Because the P-value is greater than α, there is not sufficient evidence that the prices of hotel rooms from site A and site B are different, on average.

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Transcript

00:01 Now here in this question, basically you look at 32 hotel ruins across estate, right? and that's the price of each room from side a and start b, right? so you have 32 hotel rooms.

00:15 And the main difference for the sample is 5 .49 with a standard deviation of 18 .65, right? so basically you ask you to, you ask you to test the hypothesis that whether the, you know, the prices of hotel rooms from the a and b are different, right? so basically the non -hypothesis i'm going to take, of course, the price are the same.

00:49 So in other words, the difference is not different from zero, right? so the actual difference, the actual difference, the difference, the mean, the difference between the means, which i call mua equals zero, right? and the alternative hypothesis is of course the muo not equals zero.

01:07 So we have to do a two -sided test.

01:10 The all of our significance level is 5 % according to question.

01:14 So we have to find the p value and the critical value, right? so the critical value is, of course, determined by, and it's of course determined by the t score, at actually the significance level over 2, right? so that's given by 5 % over 2, there's 2 .5%.

01:33 And then at the graphidum, which is 32, minus 1, 31, right? so if you look up the key table, you'll find this to be about 1 .65.

01:45 And then we need to find the p value.

01:47 To do that, we need to calculate the test, it has the value, right? it has a statistic, which i call t, right? and that's given by, of course, the sample mean, which is 5 .49, divided by the sample standard relation 18 .50, 65, and divided by the scruiter of sample size, which is 32.

02:07 And you found this to be given by 1 .67.

02:20 So that's my test value...

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