Statistics Techniques

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Answer th 5 questions below thoroughly

 

 

1) The Appliance Center has six sales representatives at its North Jacksonville outlet.

Listed below is the number of refrigerators sold by each last month.

 

Sales Rep        Number Sold                                                                   

Zina Craft               54                                            

Woon Junge          50                                            

Ernie DeBrul          52                                            

Jan Niles                48                                            

Molly Camp           50                                            

Rachel Myak         52                                            

                                                                         

a. How many samples of size 2 are possible?                        

b. Select all possible samples of size 2 and compute the mean number sold.

c. Organize the sample means into a frequency distribution.              

d. What is the mean of the population? What is the mean of the sample means?

e. What is the shape of the population distribution?                

f. What is the shape of the distribution of the sample mean?

 

Create the graphs from both distributions?

 

2) The manufacturer of a new line of ink-jet printers would like to include as part of its advertising the number of pages a user can expect from a print cartridge. A sample of 10 cartridges revealed the following number of pages printed.

 

(note - Excel's Data Analysis has an option under Descriptive Statistics that will allow a Confidence Interval to be calculated from a set of raw data) 

2,698    2,028    2,474     2,395     2,372     2,475     1,927     3,006     2,334     2,379

 

a. What is the point estimate of the population mean?

 

b. Develop a 95% confidence interval for the population mean.

 

3) Ms. Maria Wilson is considering running for mayor of the town of Bear Gulch, Montana.

Before completing the petitions, she decides to conduct a survey of voters in Bear Gulch. A

sample of 400 voters reveals that 300 would support her in the November election.

Estimate the value of the population proportion.

Develop a 99% confidence interval for the population proportion.

Interpret your findings.

 

4) Define a hypothesis

Explain the process of testing a hypothesis.

Distinguish between a one-tailed and a two-tailed test of hypothesis.

 

5) Heinz, a manufacturer of ketchup, uses a particular machine to dispense 16 ounces of its ketchup into containers. From many years of experience with the particular dispensing machine, Heinz knows the amount of product in each container follows a normal distribution with a mean of 16 ounces and a standard deviation of 0.15 ounce. A sample of 50 containers filled last hour revealed the mean amount per container was 16.017 ounces. Does this evidence suggest that the mean amount dispensed is different from 16 ounces? Use the .05 significance level.

 

 (a) State the null hypothesis and the alternate hypothesis. 

    (b) What is the probability of a Type I error?

    (c) Give the formula for the test statistic.

    (d) State the decision rule.

    (e) Determine the value of the test statistic.

    (f) What is your decision regarding the null hypothesis?  

    (g) Interpret, in a single sentence, the result of the statistical test.

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