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. Proctored Nonproctored μ μ1 μ2 n 32 33 x 75.91 88.05 s 10.92 18.37 a. Use a 0.01 significance level to 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. H0: μ1=μ2 H1: μ1≠μ2 B. H0: μ1=μ2 H1: μ1>μ2 C. H0: μ1≠μ2 H1: μ1<μ2 D. H0: μ1=μ2 H1: μ1<μ2 The test statistic, t, is negative 3.28−3.28. (Round to two decimal places as needed.) The P-value is 0.00010.0001. (Round to three decimal places as needed.) State the conclusion for the test. A. Fail to reject H0. 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 H0. 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. Fail to reject H0. There is not sufficient evidence to support the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests. D. Reject H0. There is 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. 22.1422.14<μ1−μ2

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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.			Proctored	Nonproctored
μ	μ1	μ2
n	32	33
x	75.91	88.05
s	10.92	18.37

a. Use a

0.01

significance level to 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?

H0:

μ1=μ2

H1:

μ1≠μ2

H0:

μ1=μ2

H1:

μ1>μ2

H0:

μ1≠μ2

H1:

μ1<μ2

H0:

μ1=μ2

H1:

μ1<μ2

The test statistic, t, is

negative 3.28−3.28.

(Round to two decimal places as needed.)

The P-value is

0.00010.0001.

(Round to three decimal places as needed.)

State the conclusion for the test.

Fail to reject

H0.

There

sufficient evidence to support the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests.

Reject

H0.

There

is not

sufficient evidence to support the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests.

Fail to reject

H0.

There

is not

sufficient evidence to support the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests.

Reject

H0.

There

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.

22.1422.14<μ1−μ2<negative 2.14−2.14

(Round to two decimal places as needed.)

Does the confidence interval support the conclusion of the test?

No,

Yes,

No,

because the confidence interval contains

only negative values.

only positive values.

only negative values.

zero.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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