Test the claim that the mean GPA of night students is larger than 2 at the .025 significance level.The null and alternative hypothesis would be:H0:p=0.5H1:p<0.5H0:μ=2H1:μ≠2H0:p=0.5H1:p≠0.5H0:μ=2H1:μ>2H0:μ=2H1:μ<2H0:p=0.5H1:p>0.5Based on a sample of 60 people, the sample mean GPA was 2.03 with a standard deviation of 0.06The test statistic is (to 3 decimals)The critical value is (to 3 decimals)Based on this wereject the null hypothesisfail to reject the null hypothesis

Solution: Let X be the GPA of night student. From the given information, x-bar=2.03, S=0.06 and n=60.The given claim is that the mean GPA of night students is larger than 2. State the hypotheses. Null hypothesis: H0: µ=2 That is, the mean GPA of night student is not larger than 2. Alternative hypothesis: H1: µ>2 That is, the mean GPA of night student is larger than 2. Here, the test is right-tailed. Thus, the correct option is “H0: µ=2 and H1: µ>2”.The test statistic is Thus, the test statistic is 3.873. The critical value is Thus, the critical value is 2.001.Rejection rule: If the test statistic value is greater than 2.001, then reject the null hypothesis. Conclusion: Here, the test statistic is 3.873. This is greater than 2.001. By the rejection rule, reject the null hypothesis. Thus, the correct option is “reject the null hypothesis”.

Answered: Test the claim that the mean GPA of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Test the claim that the mean GPA of night students is larger than 2 at the .025 significance level.

The null and alternative hypothesis would be:

H0:p=0.5
H1:p<0.5
H0:μ=2
H1:μ≠2
H0:p=0.5
H1:p≠0.5
H0:μ=2
H1:μ>2
H0:μ=2
H1:μ<2
H0:p=0.5
H1:p>0.5

Based on a sample of 60 people, the sample mean GPA was 2.03 with a standard deviation of 0.06

The test statistic is (to 3 decimals)

The critical value is (to 3 decimals)

Based on this we

reject the null hypothesis
fail to reject the null hypothesis

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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