1) A simple random sample of 100 observations was taken from a large population.

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Question

1) A simple random sample of 100 observations was taken from a large population. The sample mean and the standard deviation were determined to be 80 and 12 respectively. Using Excel, the standard error of the mean is...

2) A random sample of 16 students selected from the student body of a large university had an average age of 25 years and a standard deviation of 2 years. We want to determine if the average age of all the students at the university is significantly more than 24. Assume the distribution of the population of ages is normal. Using Excel (at 95% confidence level) it can be concluded that the mean age is…

Explanation / Answer

Question 1

Solution:

We are given n = 100

Xbar = 80

S = 12

Standard error = S/sqrt(n) = 12/sqrt(100) = 12/10 = 1.2

Standard error = 1.2

Question 2

We are given

Sample size = n = 16

Xbar = 25

S = 2

C = 0.95, = 1 – 0.95 = 0.05

H0: µ = 24 versus Ha: µ > 24

Here, we have to use one sample t test for population mean. The test by using excel is given as below:

Data

Null Hypothesis m=

Level of Significance

0.05

Sample Size

Sample Mean

Sample Standard Deviation

Intermediate Calculations

Standard Error of the Mean

0.5000

Degrees of Freedom

t Test Statistic

2.0000

Upper-Tail Test

Upper Critical Value

1.7531

p-Value

0.0320

Reject the null hypothesis

We reject the null hypothesis that the average age of all the students at the university is 24 years.

So, there is sufficient evidence to conclude that the average age of all the students at the university is more than 24 years.