(a) State the null and alternative hypotheses. Let mu be the mean score. Choose
ID: 3289355 • Letter: #
Question
(a) State the null and alternative hypotheses. Let
mu
be the mean score. Choose the correct answer below.
A.
Upper H 0 : mu less than 517H0: <517,
Upper H 1 : mu greater than 517H1: >517
B.
Upper H 0 : mu equals 517H0: =517,
Upper H 1 : mu not equals 517H1: 517
C.
Upper H 0 : mu greater than 517H0: >517,
Upper H 1 : mu not equals 517H1: 517
D.
Upper H 0 : mu equals 517H0: =517,
Upper H 1 : mu greater than 517H1: >517(b) Test the hypothesis at the
alpha equals=0.100.10
level of significance. Is a mean math score of
524524
statistically significantly higher than
517517?
Conduct a hypothesis test using theP-value approach.
Find the test statistic.
t 0t0equals=nothing
(Round to two decimal places as needed.)
Find the P-value.
The P-value is
nothing.
(Round to three decimal places as needed.)
Is the sample mean statistically significantly higher?
YesYes
NoNo
(c) Do you think that a mean math score of
524524
versus
517517
will affect the decision of a school admissions administrator? In other words, does the increase in the score have any practical significance?
Yes, because every increase in score is practically significant.
No, because the score became only
1.351.35%
greater.(d) Test the hypothesis at the
alphaequals=0.10
level of significance with
nequals=350350
students. Assume that the sample mean is still
524524
and the sample standard deviation is still
115115.
Is a sample mean of
524524
significantly more than
517517?
Conduct a hypothesis test using the P-value approach.
Find the test statistic.
t 0t0equals=nothing
(Round to two decimal places as needed.)
Find the P-value.
The P-value is
nothing.
(Round to three decimal places as needed.)
Is the sample mean statistically significantly higher?
YesYes
NoNo
What do you conclude about the impact of large samples on the P-value?
A.
As n increases, the likelihood of rejecting the null hypothesis increases. However, large samples tend to overemphasize practically insignificant differences.
B.
As n increases, the likelihood of rejecting the null hypothesis increases. However, large samples tend to overemphasize practically significant differences.
C.
As n increases, the likelihood of not rejecting the null hypothesis increases. However, large samples tend to overemphasize practically significant differences.
D.
As n increases, the likelihood of not rejecting the null hypothesis increases. However, large samples tend to overemphasize practically insignificant differences.
Click to select your answer(s).
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
=517.
The teacher obtains a random sample of
1800
students, puts them through the reviewclass, and finds that the mean math score of the
1800
students is
524
with a standard deviation of
115
Complete parts (a) through (d) below.
Explanation / Answer
The claim is that the Scores increases after taking the course
.
Answer to part a)
the null hypothesis is : M = 517
Alternate hypothesis is : M > 517
Thus the correct answer choice is D
.
Answer to part b)
n = 1800
Alpha = 0.10
x = 524
mean (M) = 517
s = 115
Z = (524 -517) / (115/sqrt(1800))
Z = 2.58
.
The right tailed P value is : 1 -0.9951 = 0.0049
.
Inference: Since the P value 0.0049 < 0.10 , thus we reject the null hypothesis
.
Conclusion: Thus we conclude that the mean score is higher than 517. there is statistically significant difference.
Hence the answer to part B is YES
.
Answer to part c)
yes , the score is statistically significant
.
Answer to part d)
n = 350
z = (524 -517) / (115/sqrt(350))
z = 1.139
.
The right tailed P value is 0.1274
.
Inference: Since the P value 0.1274 > alpha 0.10 , we fail to reject the null hypothesis
.
Conclusion: Thus we conclude that the value 524 is not significantly more than 517
The correct answer choice is A
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