Very important: SHOW ALL WORK to get full credit (i.e., correct answer without clear path leading to the answer will NOT be accepted).
Problem 1
You are given the following information obtained from a random sample of 4 observations.
25 
47 
32 
56 
You want to determine whether or not the mean of the population from which this sample was taken is significantly different from 48. (Assume the population is normally distributed.)
a. State the null and the alternative hypotheses. H0= M HA=M
b. Determine the test statistic.
c. Determine the pvalue; and at 95% confidence test to determine whether or not the mean of the population is significantly different from 48.
Problem 2
The reliability of two types of machines used in the same manufacturing process is to be tested. The first machine failed to operate correctly in 90 out of 300 trials while the second type failed to operate correctly in 50 out of 250 trials.
a. 
Give a point estimate for the difference between the population proportions of these machines. 
b. 
Calculate the pooled estimate of the population proportion. 
c. 
Carry out a hypothesis test to check whether there is a statistically significant difference in the reliability for the two types of machines using a .10 level of significance. 
Problem 3
In order to estimate the difference between the average Miles per Gallon of two different models of automobiles, samples are taken and the following information is collected.

Model A 
Model B 
Sample Size 
60 
55 
Sample Mean 
28 
25 
Sample Variance 
16 
9 


a. Test if one model gets a higher MPG than the other at 95% confidence.
b. 
At 95% confidence develop an interval estimate for the difference between the average Miles per Gallon for the two models. 


Subject  Mathematics 
Due By (Pacific Time)  09/18/2014 02:08 am 
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