Based on the summary of the data below, please answer those questions: Question

Question

Based on the summary of the data below, please answer those questions:

Question #1. Report the number of students and the percentage of students with a GPA above 2.6.

Question #2. Explain how to find in StatCrunch how to arrive at the 95% confidence interval of the mean GPA for students above 2.6 GPA and the proportion (percentage) of students who have a GPA above 2.6. Provide the answer to this question.

Question #3. – Report your interpretation of the confidence interval for the mean number of students as well as the proportion of students who have a GPA above 2.6. Provide the answer to the question.

Column n Mean Variance Std. dev. Std. err. Median Range Min Max Q1 Q3 Age 3877 27.305391 106.13685 10.302274 0.16545702 23 68 14 82 20 31 Full or Part Time 7 0 0 0 0 0 0 0 0 0 0 GPA 3877 2.6317591 1.0764702 1.0375308 0.016662997 2.85 4 0 4 2.18 3.36 Earned Credit Hours 3877 32.687645 523.5087 22.880313 0.36746337 28 161 3 164 12 48 High School Graduation Year 3732 2009.0019 87.900023 9.3755012 0.15347007 2012 64 1953 2017 2006 2016

Explanation / Answer

We have given that the summary statistics of the data.

Question #1. Report the number of students and the percentage of students with a GPA above 2.6.

For GPA,

mean = 2.63

sd = 1.0375

se = 0.017

Now we have to find P(X > 2.6) and next to find percentage and to find number of students whose GPA is > 2.6

COnvert x = 2.6 into z-score.

z = (x - mean) / sd = (2.6 - 2.63) / 1.0375 = -0.03

Now we have to find P(Z > -0.03)

This probability we can find in excel.

syntax :

=1 - NORMSDIST(z)

where z is z-score.

P(Z > -0.03) = 0.5115

Percentage = 0.5115*100 = 51.15%

And number of students whose GPA is more than 2.6 = 0.5115*3877 = 1983.22 which is approximately equal to 1983.

Question #2. Explain how to find in StatCrunch how to arrive at the 95% confidence interval of the mean GPA for students above 2.6 GPA and the proportion (percentage) of students who have a GPA above 2.6. Provide the answer to this question.

COnfidence interval we can find in ti-83 calculator.

steps :

1. If you have raw data, enter them into the spreadsheet. Name the column variable.

2. Select Stat, highlight T Statistics, select One sample, and then choose either with data or with summary.

3. If you chose with data, select the column that has the observations, then click Next>. If you chose with summary, enter the mean, standard deviation, and sample size. Click Next>.

4. Choose the confidence interval radio button. Enter the level of confidence. Click Calculate.

95% confidence interval for population mean is (2.5973, 2.6627).

We are 95% confident that population mean is lies between 2.5973 and 2.6627.

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