MATH227 Fall 2009 HWK#07
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1. Some colleges (like UCLA) have pushed back the starting time of morning classes because students were not getting enough sleep. A random sample of 20 college students had an average of 6.54 hours of sleep and somehow we know that the standard deviation of the population is 1.90 hours. Assuming the population is normally distributed. Test the claim that the true mean amount of sleep that college students get per night is not 7 hours. Use 0.05 level of significant.
2. “While vast majorities of Americans experience a range of rude behaviors at least occasionally in their daily lives, the one transgression that occurs most often is accompanied by a ring tone: people talking on cell phones in public places in a loud or annoying manner.” An ABC news poll was conducted by telephone (Jan. 20-24, 2006) among a random national sample of 1014 adults. Of those sampled, 600 said that they often see people making annoying cell phone calls. Test the claim that the true proportion of American adults that often see people making annoying cell phone calls is more than 55%. Use 0.02 level of significant..
3. A sample of 50 VISA accounts was selected and the amount of unpaid balance was observed. The mean was $960 with a standard deviation of $200. Test the claim that the true mean amount of unpaid VISA balances is less than $1000. Use 0.01 level of significant.
4. You are interested in purchasing a house in a new subdivision. You are interested in the average size of the homes and in the amount of variation in the size of homes. In a random sample of 20 homes, you find a sample mean of 2200 square feet and a standard deviation of 400 square feet. Test the claim that the true mean size of all homes in the area you are looking is more than 2000 square feet. Use 0.05 level of significant. Assuming that the size of homes is approximately normally distributed..
5. Below is the age of a random sample of 12 students at ELAC.
20 25 26 36 45 18
19 21 28 27 19 21
It is assumed that the distribution of all such students is normally distributed.
a. Find the mean and standard deviation of this sample.
b. Test the claim that the true mean age of all students age at ELAC is not 26 years.
c. Test the claim that the true standard deviation age of all students age at ELAC is not 6 years..
d. Can we solve this problem without the normality assumptions?
6-Below is the age of a random sample of 36 students at ELAC.
28 / 21 / 30 / 22 / 29 / 2624 / 29 / 23 / 17 / 33 / 28
34 / 17 / 41 / 18 / 35 / 18
16 / 37 / 32 / 27 / 46 / 31
25 / 34 / 20 / 39 / 21 / 8
29 / 32 / 34 / 33 / 42 / 25
a. Find the mean and standard deviation of this sample.
b. Test the claim that the true mean age of all students age at ELAC is not 26 years.
c. Test the claim that the true standard deviation age of all students age at ELAC is not 6 years.
d. Can we solve this problem without the normality assumptions?
7. In a medical study, the temperatures of 20 women were measured, generating the following results:
97.8 97.2 97.4 97.6 97.8 97.9 98.0 98.0 98.0 98.1
98.2 98.3 98.3 98.4 98.4 98.4 98.5 98.6 98.6 98.7
Does this sample support the hypothesis that the standard deviation of the temperatures is not 0.65? Assume the data is normally distributed.
8. For the fourth semester in a row, you’ve had to take a final on early morning. You decide to protest. Sadly, the Provost will only listen to your complaint if you can prove that more than 70% of the student population is unhappy with early morning finals. In a random sample of 1000 students, you find that 750 would like to eliminate early morning finals. At the 0.005 level, is there sufficient evidence to bring your complaint before the Provost?
9. A report in USA Today claimed that the mean age of commercial jets in the United States was 14 years. An executive of a large airline company does not believe that this is accurate. He samples 36 planes and finds the average ages of the planes is 12.6 years with a standard deviation of 2.7 years. At the 0.05 level, is their support for the executive’s claim?
10. Before a baseball bat is approved by the NCAA for use, it goes through a lengthy testing procedure. The baseballs used during testing must have a mass of 145.4 grams. If the standard deviation of the weight of the baseballs exceeds 1 gram, then they cannot be used. Suppose that in a sample of 30 baseballs that are to be used for testing, the standard deviation is found to be 1.037 grams. Based on this information, can the lot of baseballs be used? Assuming that the weights of baseballs are normally distributed, test the appropriate hypothesis at the 0.01 level.
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