Questions 1-7 Previously a study found that Statistics students were spending about $400.00 on textbooks per semester.A researcher at Penn State decides to research book cost because he now believes that book cost per semester is greater than $400.00.A random sample of 64 Statistics students finds that the sample average is $410.00 with a standard deviation of $80.Is this strong evidence that the average amount spent on textbooks per semester is greater than $400?We wish to carry out the appropriate hypothesis test.

1.In this situation, the null hypothesis is that:

the long run average equals $400

the long run average is greater than $400

the long run average is greater than $410

the long run average equals $410

2.The standard error of the mean under the null hypothesis is:

$10

$80

$20

$15

3.What is our test statistic value (standardized score)?

+1.0

+0.5

-1.0

-0.5

4.What is the p-value of our test statistic (standardized score) for the significance test?

0.16 or 16%

0.31 or 31%

0.84 or 84%

0.69 or 69%

5.Based on the p-value, we can conclude:

that the null hypothesis is a reasonable explanation of the data

that the null hypothesis is a poor explanation of the data

that the null hypothesis is true

that the alternative hypothesis is true

6.What is the Type 2 error in this situation?

fail to reject that the population average is $400 when we should reject that the population average is $400

reject that the population average is $400 when we should not reject that the population average is $400

7.Given the p-value found in our hypothesis test, would a 95% confidence interval for the true population average spent include $400?

Yes

No

8.What would the p-value be if our alternative hypothesis was that textbook costs are "different than" $400 instead of "greater than" $400? (Note: we consider a hypothesis test where we are testing whether the population value is greater than (>) some value to be a one-sided test.When we test to see if the population value is different (not equal to) some value, then we have a two-sided test)

the same as the p-value we found for the one-sided test less than the p-value we found for the one-sided test

less than the p-value we found for the one-sided test

greater than the p-value we found for the one-sided test

cannot tell until we calculate the p-value

9.If the sample size was increased and instead of randomly selecting 64 students, 225 students were randomly selected.The p-value of our test statistic (standardized score) would___

be larger than before

be smaller than before

be the same as before

cannot tell from the information given