Attitudes Refer to Exercise 4. In the study of older students’ attitudes, the sample mean SSHA score was 125.7 and the sample standard deviation was 29.8. A significance test yields a P-value of 0.0101.
a. Explain what it would mean for the null hypothesis to be true in this setting.
b. Interpret the P-value.
Part a) The correct mean score for the students who are at least years of age is
Part b) The P-value is if the population mean is equal to, then there is the possibility ofof getting a random sample with a sample mean of or more.
From the previous exercise,
is the population mean score of students who are at least 30 years of age.
If the null hypothesis is correct, the true mean score for students who are at least years old is
Result of the previous exercise:
If the population means is then there is a chance of getting a random sample with a sample means of or higher.
Aconfidence interval for the proportion of viewers of a certain reality television
show who are over 30 years old is . Suppose the show's producers want to est the hypothesis against Ha: . Which of the following is an appropriate conclusion for them to draw at the
a. Fail to reject ; there is convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old equals
b. Fail to reject there is not convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old differs from
c. Reject ; there is not convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old differs from
. d. Reject ; there is convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old is greater than
e. Reject ; there is convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old differs from.
Fire the coach! A college president says, “More than two-thirds of the alumni support my firing of Coach Boggs.” The president’s statement is based on emails he has received from alumni in the past three months. The college’s athletic director wants to perform a test of versus , where = the true proportion of the college’s alumni who favor firing the coach. Check if the conditions for performing the significance test are met.
Teen drivers Refer to Exercise 51.
a. Construct and interpret a 95% confidence interval for the true proportion p of all teens in the state who passed their driving test on the first attempt. Assume that the conditions for inference are met.
b. Explain why the interval in part (a) provides more information than the test in Exercise 51.
Potato chips A company that makes potato chips requires each shipment of
potatoes to meet certain quality standards. If the company finds convincing evidence that more than of the potatoes in the shipment have “blemishes,” the truck will be sent back to the supplier to get another load of potatoes. Otherwise, the entire truckload will be used to make potato chips. To make the decision, a supervisor will inspect a random sample of potatoes from the shipment. He will then perform a test of versus , where p is the true proportion of potatoes with blemishes in a given truckload. The power of the test to detect that , based on a random sample of potatoes and significance level , is Interpret this value.
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