Project #75600 - Stastics

 

1. (4 points) An important component in the evaluating confidence interval and performing hypothesis test is the critical value, and the critical value depends on what distribution we should apply. Please fill in the corresponding distribution in the following table.

 

Parameter

Requirements

Distribution for the Critical Value

Proportion p

(1) simple random sample
(2) conditions for the binomial distribution are satisfied
(3) np >= 5 and nq >= 5

 

 

 

 

Mean μ

(1) simple random sample
(2) the population is normally distributed or n > 30
(3) population standard deviation σ is unknown

 

 

 

 

Mean μ

(1) simple random sample
(2) the population is normally distributed or n > 30
(3) population standard deviation σ is known

 

 

 

 

Standard deviation σ

(1) simple random sample
(2) the population is normally distributed

 

 

 

 

2.  (15 points)  Mimi was the 5th seed in 2014 UMUC Tennis Open that took place in August.  In this tournament, she won 75 of her 100 serving games. Based on UMUC Sports Network, she wins 80% of the serving games in her 5-year tennis career.

 

(a) (3 pts) Find a 90% confidence interval estimate of the proportion of serving games Mimi won. (Show work and round the answer to three decimal places)

 

 

 

 

 

 

 

 

 

(b) (2 pts) Based on the confidence interval estimate you got in part (a), is this tournament result consistent with her career record of 80%?  Why or why not?  Please explain your conclusion.

 

 

 

 

 

Parts (c) through (g): A sport reporter commented that Mimi’s performance in the tournament is worse than her career average of 80%. You decide to test if the reporter’s claim is valid by using hypothesis testing that you just learned from STAT 200 class.

 

(c) (2 pts) What are your null and alternative hypotheses?

 

 

 

 

 

(d) (2 pts) What is the test statistic? (Show work and round the answer to two decimal places)

 

 

 

 

 

 

 

 

 

 

 

(e) (2 pts) What is the P-value? (Show work and express the answer in four decimal places)

 

 

 

 

 

 

 

(f) (2 pts) What is the critical value if you perform the test at 0.10 significance level? (Show work)

 

 

 

 

 

 

 

(g) (2 pts) What is your conclusion of the testing at 0.10 significance level? Why?

 

 

 

 

 

3.  (5 points)  A simple random sample of 120 SAT scores has a sample mean of 1540. Assume that SAT scores have a population standard deviation of 300.

 

(a) (4 pts) Construct a 95% confidence interval estimate of the mean SAT score. (Show work and round the answer to two decimal places)

 

 

 

 

 

 

 

 

 

 

 

(b) (1 pt) Is a 90% confidence interval estimate of the mean SAT score wider than the 95% confidence interval estimate you got from part (a)? Why? [You don’t have to construct the 90% confidence interval]

 

 

 

 

 

4.  (5 points)  Consider the hypothesis test given by                                               

 

           

 

In a random sample of 70 subjects, the sample mean is found to be  The population standard deviation is known to be     

 

  1. (1 pt) Is this test for population proportion, mean or standard deviation? What distribution should you apply for the critical value?

 

 

 

  1. (3 pts) Determine the P-value for this test.  (Show work and round the answer to three decimal places)

     

     

     

     

     

     

     

  2. (1 pt) Is there sufficient evidence to justify the rejection of  at the  level? Explain.                           

 

 5. (6 pts) The playing times of songs are normally distributed. Listed below are the playing times (in seconds) of 5 songs from a random sample. Use a 0.05 significance level to test the claim that the songs are from a population with a standard deviation less than 1 minute.

 

 

 

450   250  200  200  400

 

 

 

(a) (1 pt) What are your null hypothesis and alternative hypothesis?

 

 

 

 

 

 

 

 

 

  1. (1 pt) Is this test for population proportion, mean or standard deviation? What distribution should you apply for the critical value?

 

 

 

 

 

 

 

 

 

(c) (2 pts) What is the test statistic? (Show work and round the answer to two decimal places)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  1. (2 pts) What is your conclusion? Why? (Show work)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6. (5 pts) Assume the population is normally distributed. Given a sample size of 25, with sample mean 740 and sample standard deviation 80, we perform the following hypothesis test.

 

           

 

 

  1.  (1 pt) Is this test for population proportion, mean or standard deviation? What distribution should you apply for the critical value?

     

     

     

  2. (2 pts) What is the test statistic? (Show work and round the answer to three decimal places)

     

     

     

     

     

     

  3. (2 pts) What is your conclusion of the test at the α = 0.10 level? Why? (Show work)

 

Subject Mathematics
Due By (Pacific Time) 07/05/2015 11:00 pm
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