You are testing the claim that the mean GPA of night students is different from the mean GPA of day students. You sample 30 night students, and the sample mean GPA is 2.83 with a standard deviation of 0.94. You sample 55 day students, and the sample mean GPA is 2.97 with a standard deviation of 0.92. Test the claim using a 1% level of significance. Assume the population standard deviations are unequal and that GPAs are normally distributed. Give answer to at least 4 decimal places. What are the correct hypotheses? H0: Select an answer μ σ² μ₂ p μ₁ x̄₂ s² x̄₁ = Select an answer μ x̄₂ σ² μ₂ x̄₁ μ₁ s² p H1: Select an answer σ² μ x̄₁ s² p x̄₂ μ₁ μ₂ ? = < > ≤ ≠ ≥ Select an answer μ x̄₂ x̄₁ μ₂ σ² s² μ₁ p Based on the hypotheses, find the following: Test Statistic = Critical Values = ±± (Just enter the positive CV.) The correct decision is to Select an answer Reject the null hypothesis Fail to reject the null hypothesis The correct summary would be: Select an answer There is not enough evidence to support the claim There is not enough evidence to reject the claim There is enough evidence to support the claim There is enough evidence to reject the claim that the mean GPA of night students is different from the mean GPA of day students.
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.
You are testing the claim that the
What are the correct hypotheses?
H0: Select an answer μ σ² μ₂ p μ₁ x̄₂ s² x̄₁ = Select an answer μ x̄₂ σ² μ₂ x̄₁ μ₁ s² p
H1: Select an answer σ² μ x̄₁ s² p x̄₂ μ₁ μ₂ ? = < > ≤ ≠ ≥ Select an answer μ x̄₂ x̄₁ μ₂ σ² s² μ₁ p
Based on the hypotheses, find the following:
Test Statistic =
Critical Values = ±± (Just enter the positive CV.)
The correct decision is to Select an answer Reject the null hypothesis Fail to reject the null hypothesis
The correct summary would be: Select an answer There is not enough evidence to support the claim There is not enough evidence to reject the claim There is enough evidence to support the claim There is enough evidence to reject the claim that the mean GPA of night students is different from the mean GPA of day students.
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