Question
In: Statistics and Probability
1. Suppose a researcher is testing the hypothesis Upper H 0: pequals0.6 versus Upper H 1:...
1. Suppose a researcher is testing the hypothesis Upper H 0: pequals0.6 versus Upper H 1: p less than0.6 and she finds the?P-value to be 0.24. Explain what this means. Would she reject the null?hypothesis? Why?
Choose the correct explanation below.
If the?P-value for a particular test statistic is 0.24, she expects results no more extreme than the test statistic in about 24 of 100 samples if the null hypothesis is true.
If the?P-value for a particular test statistic is 0.24, she expects results at least as extreme as the test statistic in about 24 of 100 samples if the null hypothesis is true.
If the?P-value for a particular test statistic is 0.24, she expects results at least as extreme as the test statistic in exactly 24 of 100 samples if the null hypothesis is true.
D. If the?P-value for a particular test statistic is 0.24, she expects results no more extreme than the test statistic in exactly 24 of 100 samples if the null hypothesis is true.
1. Choose the correct conclusion below.
A.Since this event is?unusual, she will reject the null hypothesis.
B.Since this event is?unusual, she will not reject the null hypothesis.
C.Since this event is not?unusual, she will reject the null hypothesis.
D.Since this event is not?unusual, she will not reject the null hypothesis.
2. The mean consumption of fruit three years ago was 98.5 pounds. A dietician believes that fruit consumption has fallen since then.
?(a) Determine the null and alternative hypotheses. Which of the following is?correct?
A. Upper H 0: mu equals98.5; Upper H 1: mu less than98.5
B. Upper H 0: mu equals98.5; Upper H 1: mu not equals98.5
C. Upper H 0: mu equals98.5; Upper H 1: mu greater than98.5
?(b) Suppose sample data indicate that the null hypothesis should be rejected. State the conclusion of the researcher. Which of the following is the conclusion that could be?reached?
A. There is not sufficient evidence to conclude that the mean consumption of fruit has stayed the same.
B. There is sufficient evidence to conclude that the mean consumption of fruit has stayed the same.
C. There is not sufficient evidence to conclude that the mean consumption of fruit has fallen.
D. There is sufficient evidence to conclude that the mean consumption of fruit has fallen.
A math teacher claims that she has developed a review course that increases the scores of students on the math portion of a college entrance exam. Based on data from the administrator of the?exam, scores are normally distributed with mu equals517. The teacher obtains a random sample of 1800 students, puts them through the review?class, and finds that the mean math score of the 1800 students is 524 with a standard deviation of 110. Complete parts?(a) through?(c) below.
?(a) State the null and alternative hypotheses. Let mu be the mean score. Choose the correct answer below.
A.Upper H 0: mu greater than 517, Upper H 1: mu not equals 517
Upper H 0: mu equals 517, Upper H 1: mu greater than 517
C.Upper H 0: mu less than 517, Upper H 1: mu greater than 517
D Upper H 0: mu equals 517, Upper H 1: mu not equals 517
?(b) Test the hypothesis at the alpha equals0.10 level of significance. Is a mean math score of 524 statistically significantly higher than 517? Conduct a hypothesis test using the?P-value approach.
Find the test statistic.
t0 equals?
?(Round to two decimal places as?needed.)
Find the?P-value.
The?P-value is?
?(Round to three decimal places as?needed.)
Is the sample mean statistically significantly?higher?
No
Yes
?(c) Do you think that a mean math score of 524 versus 517 will affect the decision of a school admissions?administrator? In other?words, does the increase in the score have any practical?significance?
?A, No, because the score became only 1.35?% greater.
?B,Yes, because every increase in score is practically significant.
Solutions
Expert Solution
1. Suppose a researcher is testing the hypothesis Upper H 0: pequals0.6 versus Upper H 1: p less than0.6 and she finds the?P-value to be 0.24. Explain what this means. Would she reject the null?hypothesis? Why?
Answer: Ho: p = 0.6 and H1: p < 0.6
P- value is 0.24.
Considering alpha to be 5% or alpha = 0.05
As p-value that is 0.24 > 0.05 therefore, null hypothesis is accepted at 95% level of significance and this implies that p = 0.6
Choose the correct explanation below.
A. If the?P-value for a particular test statistic is 0.24, she expects results no more extreme than the test statistic in about 24 of 100 samples if the null hypothesis is true.
B. If the?P-value for a particular test statistic is 0.24, she expects results at least as extreme as the test statistic in about 24 of 100 samples if the null hypothesis is true.
C. If the?P-value for a particular test statistic is 0.24, she expects results at least as extreme as the test statistic in exactly 24 of 100 samples if the null hypothesis is true.
D. If the?P-value for a particular test statistic is 0.24, she expects results no more extreme than the test statistic in exactly 24 of 100 samples if the null hypothesis is true.
Answer : option B that is If the?P-value for a particular test statistic is 0.24, she expects results at least as extreme as the test statistic in about 24 of 100 samples if the null hypothesis is true.
1. Choose the correct conclusion below.
A.Since this event is?unusual, she will reject the null hypothesis.
B.Since this event is?unusual, she will not reject the null hypothesis.
C.Since this event is not?unusual, she will reject the null hypothesis.
D.Since this event is not?unusual, she will not reject the null hypothesis.
Answer : option D that is Since this event is not?unusual, she will not reject the null hypothesis.
2. The mean consumption of fruit three years ago was 98.5 pounds. A dietician believes that fruit consumption has fallen since then.
?(a) Determine the null and alternative hypotheses. Which of the following is?correct?
A. Upper H 0: mu equals98.5; Upper H 1: mu less than98.5
B. Upper H 0: mu equals98.5; Upper H 1: mu not equals98.5
C. Upper H 0: mu equals98.5; Upper H 1: mu greater than98.5
Answer : option A that is Upper H 0: mu equals98.5; Upper H 1: mu less than98.5
(b) Suppose sample data indicate that the null hypothesis should be rejected. State the conclusion of the researcher. Which of the following is the conclusion that could be?reached?
A. There is not sufficient evidence to conclude that the mean consumption of fruit has stayed the same.
B. There is sufficient evidence to conclude that the mean consumption of fruit has stayed the same.
C. There is not sufficient evidence to conclude that the mean consumption of fruit has fallen.
D. There is sufficient evidence to conclude that the mean consumption of fruit has fallen.
Answer : option D that is There is sufficient evidence to conclude that the mean consumption of fruit has fallen.
A math teacher claims that she has developed a review course that increases the scores of students on the math portion of a college entrance exam. Based on data from the administrator of the?exam, scores are normally distributed with mu equals517. The teacher obtains a random sample of 1800 students, puts them through the review?class, and finds that the mean math score of the 1800 students is 524 with a standard deviation of 110. Complete parts?(a) through?(c) below.
?(a) State the null and alternative hypotheses. Let mu be the mean score. Choose the correct answer below.
A.Upper H 0: mu greater than 517, Upper H 1: mu not equals 517
B. Upper H 0: mu equals 517, Upper H 1: mu greater than 517
C. Upper H 0: mu less than 517, Upper H 1: mu greater than 517
D. Upper H 0: mu equals 517, Upper H 1: mu not equals 517
Answer : option B that is Upper H 0: mu equals 517, Upper H 1: mu greater than 517
(b) Test the hypothesis at the alpha equals0.10 level of significance. Is a mean math score of 524 statistically significantly higher than 517? Conduct a hypothesis test using the?P-value approach.
Find the test statistic.
Answer : Test statistic = ( x_bar - mu ) / ( std_dev / sqrt(n) )
=( 524 - 517 ) / ( 110 / SQRT(1800) )
=2.70
Find the?P-value.
The?P-value is?
Answer : Since the test statistic is 2.70, we can calculate p-value using the "right of curve Z table"
and found that corresponding to 2.70 the p-value is 0.496
Is the sample mean statistically significantly?higher?
Answer : As the p-value is 0.496 therefore we accept our null hypothesis that sample mean is not statistically significantly ?higher.
?(c) Do you think that a mean math score of 524 versus 517 will affect the decision of a school admissions?administrator? In other?words, does the increase in the score have any practical?significance?
A, No, because the score became only 1.35?% greater.
?B,Yes, because every increase in score is practically significant.
Answer : option B. Yes, because every increase in score is practically significant.
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