A study was done on proctored and nonproctored tests. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a significance level 0.01 for both parts. ___________________________________________________________________ Proctored Nonproctored μ μ1 μ2 n 34 32 x 74.86 83.25 s 10.51 18.27 _______________________________________________ a) Test the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests. What are the null and alternative hypotheses? A. Ho: μ1 = μ2 H1: μ1 < μ2 B. Ho: μ1 = μ2 H1: μ1 ≠ μ2 C. Ho: μ1 = μ2 H1: μ1 > μ2 D. Ho: μ1 ≠ μ2 H1: μ1 < μ2 The test statistic, t, is____________. (Round to two decimal places as needed.) The P-value is _________ . (Round to three decimal places as needed.) State the conclusion for the test. A. Fail to reject Ho. There is sufficient evidence to support the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests. B. Reject Ho. There is not sufficient evidence to support the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests. C. Reject Ho. There is sufficient evidence to support the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests. D. Fail to reject Ho. There is not sufficient evidence to support the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests. b) Construct a confidence interval suitable for testing the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests. ________< μ1 − μ2 <________ (Round to two decimal places as needed.) Does the confidence interval support the conclusion of the test? (1) ________ because the confidence interval contains (2) ________ 1) Yes, No, (2) only negative values. zero. only positive values.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
A study was done on proctored and nonproctored tests. The results are shown in the table. Assume that the two samples are independent simple random samples selected from
___________________________________________________________________
Proctored Nonproctored
μ μ1 μ2
n 34 32
x 74.86 83.25
s 10.51 18.27
_______________________________________________
a) Test the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests.
What are the null and alternative hypotheses?
A. Ho: μ1 = μ2
H1: μ1 < μ2
B. Ho: μ1 = μ2
H1: μ1 ≠ μ2
C. Ho: μ1 = μ2
H1: μ1 > μ2
D. Ho: μ1 ≠ μ2
H1: μ1 < μ2
The test statistic, t, is____________.
(Round to two decimal places as needed.)
The P-value is _________ .
(Round to three decimal places as needed.)
State the conclusion for the test.
A. Fail to reject Ho. There is sufficient evidence to support the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests.
B. Reject Ho. There is not sufficient evidence to support the claim that students taking
nonproctored tests get a higher mean score than those taking proctored tests.
C. Reject Ho. There is sufficient evidence to support the claim that students taking
nonproctored tests get a higher mean score than those taking proctored tests.
D. Fail to reject Ho. There is not sufficient evidence to support the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests.
b) Construct a confidence interval suitable for testing the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests.
________< μ1 − μ2 <________
(Round to two decimal places as needed.)
Does the confidence interval support the conclusion of the test?
(1) ________ because the confidence interval contains (2) ________
1) Yes,
No,
(2) only negative values.
zero.
only positive values.
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