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# Testing of hypothesis problems

Dear OTA,

Thanks

1. Burney Watt, chief electrician for the Prescott Electrical Coop has been watching the electric bills for 10 properties in Prescottvilla, the up and coming snobby subdivision south of town. The residents there have been complaining that their "bills are just too high." Burney knows that they can afford the cost, and most of them never learned to turn off a light anyway. Help out Burney and figure out if the weekly data from these 10 homes are skewed or not, and if they are skewed in what direction. Please show all working.

\$118.20 \$67.88 \$133.40 \$88.42 \$110.34
\$76.90 \$114.56 \$127.89 \$89.34 \$129.10

2. The manager at the Prescott Ice Cream Shoppe, Donna Sorbet, (on the square, next to the Rexall Drugs) knows that her customers arrive at the rate of 10 every 30 minutes. The time between arrivals is exponentially distributed. Based on this information, what is the probability that the time between two customers arriving will exceed 6 minutes?

3. Pete Petro, manager of the Prescott Gasoline Company recently conducted a random study at his gas station on North Main Street to estimate the mean gallons of gas purchased by customers per visit to all his stations. He found the following number of gallons purchased by drivers during his random one-day survey was:

8.7 8.9
22 13.3
5.7 19
22.4 22.5
14.4 18.9
15.7 24.9
9.5 15.9
35.7 (Hummer)

Based on these sample data, construct and interpret a 95% confidence interval estimate for the population mean. NOTE: This is a multi-step process including finding the mean and sd. Remember to show your work and tell what the results mean.

4. The Prescott Swamp Water Bottling Company also bottles soft drinks, their Swampy Diet Cola Drink with a tinge of Alligator, is a local favorite among the teenage set. (They will drink anything.) The company uses an automatic filling machine to do the bottling. When the machine is working properly (which seems to be rarely), the mean fill is 12 ounces per can with a standard deviation of 0.20 ounces. Each day Rusty Springs selects a random sample of 36 cans and measures the volume in each can. He then tests to determine whether the filling process is working properly. The test is conducted at the 0.05 significance level. So what is the critical value in ounces? (NOTE: Here you are not looking to accept or reject the null, just give me the range. Also, I'd start by writing out the hypotheses - it's easier.)

5. The Prescott County Department of Weights and Measures supervisor, Tony Tonn, is responsible for making sure that all commercial weighing and measuring devices are working properly. As part of this he must be sure that gas stations in Prescott County actually dispense one gallon for a gallon charged. Recently he came to one of Pete Petro's Prescott Gasoline Company stations (you will remember from above). He filed 10 cans until the pump read 1.0 gallons, and then he measured precisely the amount of gasoline in each can. He found the following data:

0.991 0.962 1.007 1.038 1.036
1.052 0.934 0.993 1.033 0.967

Based on this data, at the .05 level of significance, did Pete Petro either cheat himself or his customers if the standard deviation allowable by law is 0.010 gallons per gallon of gas?

Write the hypotheses and this is a chi square test. Show all working.

Who is being hurt more, the customer or the company and why???

#### Solution Preview

Homework Assignment

1. Burney Watt, chief electrician for the Prescott Electrical Coop has been watching the electric bills for 10 properties in Prescottvilla, the up and coming snobby subdivision south of town. The residents there have been complaining that their "bills are just too high." Burney knows that they can afford the cost, and most of them never learned to turn off a light anyway. Help out Burney and figure out if the weekly data from these 10 homes are skewed or not, and if they are skewed in what direction. Please show all working.

\$118.20 \$67.88 \$133.40 \$88.42 \$110.34
\$76.90 \$114.56 \$127.89 \$89.34 \$129.10

Karl Pearson's coefficient of Skewness

Electric bills (X) (X- )2

67.88 1423.025
76.9 823.8622
88.42 295.2555
89.34 264.4852
110.34 22.43917
114.56 80.22785
118.2 158.6844
127.89 496.7104
129.1 552.109
133.4 772.6732
1056.03 4889.472
Mean =Total /N =1056.03 =105.63
Median =Mean of 5th and 6th value = 112.45
Standard deviation = = =23.5082

Skewness =3(105.63-112.45)/23.5082= -0.8703
Thus the distribution is negatively skewed.

2. The manager at the Prescott Ice Cream Shoppe, Donna Sorbet, (on the square, next to the Rexall Drugs) knows that her customers arrive at the rate of 10 every 30 minutes. The time between arrivals is exponentially distributed. Based on this information, what is the probability that the time between two customers arriving will exceed 6 minutes?