Notes: 1. Before doing this assignment, do the practice problem posted under Apply and Discover. 2. Word-process your solutions within this template. Do not create a new file. 3. Show all steps used in arriving at the final answers. Incomplete solutions will receive partial credit. 4. Word-process formulas using Equation Editor and diagrams using Drawing Tool.

Problem 1

Annual family dental expenses for the families of a random sample of ten employees of a company are given below. You can assume the family dental expenses for the employees of the company are normally distributed.

$450, $390, $550, $140, $690, $600, $250, $330, $490, $810 a) Compute the mean and standard deviation of the

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Meaning that the average for all employees should be no lower than $324.69 and no higher than $615.31.

e) These statistics can be used to show that although some employees may have high charges of say $810 or lows of $140, the majority will be between the range. It would allow the company to identify insurers that provide substantially higher prices and those that will fall within acceptable ranges.

Problem 2

The average price of regular gasoline in the continental US states and the District of Columbia was $3.74 on August 18, 2008. Alaska and Hawaii are not included as the gas prices there are much higher than the continental US. The price of gasoline in the eleven western states of the U.S. on the same day is given below. Test the hypothesis that the average price of gasoline in the western states is higher than the national average for Continental USA and the District of Columbia, i.e., higher than $3.74. Use level of significance =

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(n.d.). Retrieved August 18, 2008, from AAA: http://fuelgaugereport.opisnet.com/sbsavg.html

Step 1. Establishing a null and alternative hypothesis

The hypothesis test is based on the population mean, . This will be a one-tailed test, where the null and alternative hypothesis can be stated as follows:

Step 2. Selecting the appropriate sample size and significance

The sample size is given as 11 and the level of significance is given as

Step 3. Selecting the appropriate sample statistic and determining the rejection area.

Testing for the population mean is done by using the sample mean.

Thus , appropriate sampling distribution is the distribution of sample means.

3.74

3.74

0.05

0.05

Step 4. Selecting the appropriate test statistic Given , sample size n=11, and degrees of freedom n-1=10, looking up the t-value in the t-distribution table as shown:

Thus, the criteria is if t > 1.812, null should be