What is the probability that 2002-2003 mean tuition fees for this sample were within $550 of the population mean?

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[5 marks] j. According to Hartford Courant’s report (October 2002), the average tuition fees at private universities in the U.S. was $18,273 for the academic year 2002-2003. Suppose that the probability distribution of the 2002-2003 tuition fees at all private universities in the U.S. was unknown, but its standard deviation was $2100. Let me be the mean tuition fees for 2002-2003 for a random sample of49 private U.S. universities.

a. What is the probability that 2002-2003 mean tuition fees for this sample were within $550 of the population mean?

b. What is the probability that the 2002-2003 mean tuition fees for this sample were lower than the population mean by $400 or more?

[4 marks] 2. A candidate, who is running for mayor in a large city, claims that he is favored by 53% of all eligible voters of that city. Assume that this claim is true. Find the probability that in a random sample of 400registered voters taken from this city, less than 49% will favor the candidate.

[8 marks] 3. To evaluate the effectiveness of video-conferencing equipment in teaching, a midterm assessment was done via questionnaires. The overall satisfaction rate s, of the students which is a percentage with 100 being most satisfied was measured for students in a random sample and is shown in the text file satisfaction.txt. A model for the satisfaction of the lecture is given by Normal distribution.

a. Load the data into an R session and find the mean, standard deviation, and sample size using R code.

b. Showing all your work, compute numerically a 95% confidence interval for p in the Model.

c. Interpret the confidence interval from part (b).

d. A confidence interval in R can be calculated using the function t.test( ). (For more information, type:help(t.test)). Use the data from this question to calculate the 95% confidence interval. identify the confidence interval in the R output and include the relevant parts of your R code and output with your solution.

[4 marks] 4. Consider the data set and the confidence interval that is summarized in the following output. The

population standard deviation is not known.

One-Sample T

N Mean StDev SE Mean 95% CI

11 ? ? ? (43.9220, 60.4416)

Fill in the missing entries, and then find a 99% confidence interval for i based on the same data set.

[5 marks] 5. Consider the confidence interval given in the following output:

Test and CI for One Proportion

Test of p= 0.5 vs p not = 0.5

Sample X N Sample p ?%CI

cl 25 ? ? (0.102010, 0.224787)

What is the level of confidence? Find a 99% confidence interval for p based on the same data set.[4 marks]

6. The following set of 10 data points are independent realizations from a Binomial model x — Bin(36,p)10, 12, 7, 6, 6, 11, 7, 12, 9, 10.

Compute numerically, showing all your work, the 95% confidence interval for p

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