SEE IMAGE Answer the question. 14)A student survey was conducted at a major university. A random sample of 99 students reported data on theirgender and GPA. Summary statistics for each gender are displayed in the table below:Gender N Mean GPA StDev SE MeanFemale 59 3.21 0.51131 0.06657Male 40 2.96 0.57194 0.09043A 95% confidence interval for the mean difference in GPA between females and males (GPAF — GPAM) wascalculated to be (0.02, 0.47). Does the interval capture 0? Explain what this means (conclusion).__________________________________________________________________________________________________ **Question:**A student survey was conducted at a major university. A random sample of 99 students reported data on their gender and GPA. Summary statistics for each gender are displayed in the table below:| Gender | N | Mean GPA | StDev | SE Mean ||--------|----|----------|--------|---------|| Female | 59 | 3.21 | 0.51131 | 0.06657 || Male | 40 | 2.96 | 0.57194 | 0.09043 |A 95% confidence interval for the mean difference in GPA between females and males (GPAₒF − GPAₒM) was calculated to be (0.02, 0.47). Does the interval capture 0? Explain what this means (conclusion).---**Explanation:**The table summarizes data collected from 99 students, split into two groups based on gender: Female (59 students) and Male (40 students). For each group, the table provides the mean GPA, standard deviation (StDev), and standard error of the mean (SE Mean).The 95% confidence interval for the mean difference in GPA between females and males is calculated as (0.02, 0.47). This interval does not include 0, which suggests that there is a statistically significant difference in mean GPAs between female and male students, where female students have a higher average GPA than male students. This conclusion is drawn at the 95% confidence level, indicating there is a high probability that the true mean difference lies within this interval.

Name: SEE IMAGE Answer the question. 14)A student survey was conducted at a
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Description: SEE IMAGE Answer the question. 14)A student survey was conducted at a major university. A random sample of 99 students reported data on theirgender and GPA. Summary statistics for each gender are displayed in the table below:Gender N Mean GPA StDev S

From the given information, total number of students in the sample n = 99. Number of female students in sample nF = 59. Number of male students in sample nM = 40. From the given information, the 95% confidence interval for the mean difference in GPA between females and males (GPAF – GPAM) was (0.02, 0.47).The objective is to check whether the interval capture 0. State the null and alternative hypotheses. Null hypothesis: There is no difference in mean GPA between females and males. Alternative hypothesis: There is a difference in mean GPA between females and males. It is a two -tailed test. Decision rule: Reject the null hypothesis, if the interval does not capture zero. Conclusion: Since, the 95% confidence interval for the mean difference in GPA between females and males (GPAF – GPAM) was (0.02, 0.47). Here, the interval does not contain zero, reject the null hypothesis. Therefore, it is concluded that there is a difference in mean GPA between females and males and it is 95% confidence that the mean difference in GPA between females and males (GPAF – GPAM) was lies between 0.02 and 0.47.

Answered: 14) A student survey was conducted at a…

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SEE IMAGE

Answer the question. 14)
A student survey was conducted at a major university. A random sample of 99 students reported data on their
gender and GPA. Summary statistics for each gender are displayed in the table below:
Gender N Mean GPA StDev SE Mean
Female 59 3.21 0.51131 0.06657
Male 40 2.96 0.57194 0.09043
A 95% confidence interval for the mean difference in GPA between females and males (GPAF — GPAM) was
calculated to be (0.02, 0.47). Does the interval capture 0? Explain what this means (conclusion).
__________________________________________________________________________________________________

**Question:**

A student survey was conducted at a major university. A random sample of 99 students reported data on their gender and GPA. Summary statistics for each gender are displayed in the table below:

| Gender | N | Mean GPA | StDev | SE Mean |
|--------|----|----------|--------|---------|
| Female | 59 | 3.21 | 0.51131 | 0.06657 |
| Male | 40 | 2.96 | 0.57194 | 0.09043 |

A 95% confidence interval for the mean difference in GPA between females and males (GPAₒF − GPAₒM) was calculated to be (0.02, 0.47). Does the interval capture 0? Explain what this means (conclusion).

---

**Explanation:**

The table summarizes data collected from 99 students, split into two groups based on gender: Female (59 students) and Male (40 students). For each group, the table provides the mean GPA, standard deviation (StDev), and standard error of the mean (SE Mean).

The 95% confidence interval for the mean difference in GPA between females and males is calculated as (0.02, 0.47). This interval does not include 0, which suggests that there is a statistically significant difference in mean GPAs between female and male students, where female students have a higher average GPA than male students. This conclusion is drawn at the 95% confidence level, indicating there is a high probability that the true mean difference lies within this interval.

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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