Question

1. Dr Tiago wants to estimate the mean gpa of all incoming freshman. The mean gpa of random sample of 25 freshman is 3 with a standard deviation of 0.72. Assuming that the Gpa of all incoming freshman is normally distributed construct a 95% confidence interval for the population mean u

2. If a random sample of size 25 gives the average of 37.87 and sd of 8 calculate the test static to the test the hypothesis that average hdl-cholesterol level among the adult population of a city is atleat 39.63

Answer 1

Solution:

Question 1)

Given:

Sample Size = n = 25

Sample mean =  

Sample standard deviation = s = 0.72

the Gpa of all incoming freshman is normally distributed

We have to construct a 95% confidence interval for the population mean :

where

t_c is t critical value for c = 95%  confidence level

Thus two tail area = 1 - c = 1 - 0.95 = 0.05

df = n - 1 =  25 - 1 = 24

t_c = 2.064

Thus

Thus

.

Question 2)
Given:

Sample size = n = 25

Sample mean =

Sample standard deviation = 8

Population Mean =

We have to find test statistic value for testing mean.

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