You are testing the claim that the mean GPA of night students is different from the mean GPA of day students. A sample of 24 night students and 28 day students and their GPA's are recorded below. Test the claim using a 1% level of significance. Assume the population variances are unequal and that GPAs are normally distributed. Give answers to 4 decimal places.
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
| GPA-Night | GPA-Day |
|---|---|
| 3.05 | 3.38 |
| 2.91 | 3.02 |
| 3.27 | 3.4 |
| 3.29 | 2.73 |
| 3.3 | 3.24 |
| 3.35 | 2.69 |
| 3.39 | 3.25 |
| 3.52 | 3.33 |
| 3.39 | 2.33 |
| 3.25 | 3.51 |
| 3.08 | 3.07 |
| 3.27 | 2.9 |
| 3.32 | 3.48 |
| 3 | 2.94 |
| 3.62 | 2.93 |
| 3.64 | 3.31 |
| 3.54 | 2.62 |
| 3.45 | 2.66 |
| 3.29 | 3.27 |
| 3.56 | 2.76 |
| 3.15 | 2.7 |
| 3.4 | 3.27 |
| 3.51 | 2.96 |
| 3.54 | 2.86 |
| 3.24 | |
| 2.72 | |
| 2.64 | |
| 3.14 |
What are the correct hypotheses? Note this may view better in full screen
H0: Select an answer x̅₂ s² x̅₁ σ² μ₂ μ₁ p ? = ≠ > < ≥ ≤ Select an answer 0 μ₂ x̅₂ x̅₁ σ² p s² μ₁
H1: Select an answer σ² x̅₂ x̅₁ μ₁ μ₂ s² p ? = ≥ > ≠ ≤ < Select an answer μ₁ p s² σ² x̅₂ μ₂ 0 x̅₁
Based on the hypotheses, find the following:
Test Statistic=
p-value=
The correct decision is to
Select an answer:
reject the null hypothesis
reject the claim accept the null hypothesis
accept the alternative 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 reject the claim There is enough evidence to support the claim that the mean GPA of night students is different from the mean GPA of day students.
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