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Exam Review Questions - Probability and Statistics | MATH 1530, Exams of Probability and Statistics

Material Type: Exam; Professor: Maxson; Class: Probability and Statistics; Subject: Mathematics; University: Walters State Community College; Term: Unknown 1989;

Typology: Exams

Pre 2010

Uploaded on 08/18/2009

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Math 1530 Chapter 7 Review Questions
1. Write the null and alternative hypotheses for the following: A cereal company claims that the
mean weight of the cereal in its packets is at least 14 oz.
2a. Assume that the data has a normal distribution and sigma (σ) is not known. The sample size is
18. Find the critical t value for:
2a. Right tail test, α = 0.1. (Hint: Use Table A-3)
2b. Left tail test, α = 0.05.
2c. Two tailed test, α = 0.01
3. Find the test statistic for the following situations:
a. The claim is that the mean is 0.21; the sample statistics include: n = 32; x-bar = 0.83, s = 0.24.
b. The claim is that the mean < 1.39; sample stats include: n = 87; x-bar = 0.83; s = 0.16.
c. The claim is that the mean is at least 50; sample stats include: n = 100; x-bar = 54.8; s = 3.6
4. An entomologist writes an article in a scientific journal which claims that fewer than 7 in 10,000
(0.0007) male fireflies are unable to produce light due to a genetic mutation. Assuming that a
hypothesis test of the claim has been conducted and that the conclusion is to REJECT the null
hypothesis, state the conclusion in non-technical terms.
A. There is sufficient evidence to support the claim that the true proportion is greater than
.0007
B. There is not sufficient evidence to support the claim that the true proportion is less than
.0007
C. There is not sufficient evidence to support the claim that the true proportion is greater than
.0007
D. There is sufficient evidence to support the claim that the true proportion is less than .0007.
5. Suppose you wish to use a hypothesis test to test a claim made by a juice bottling company
regarding the mean amount of juice in its 16 oz bottles. Why does the original claim sometimes
become the null hypothesis, and why does it sometimes become the alternative hypothesis. Give
examples.
7. A store manager claims that the mean amount of time customers spend waiting in line is less
than 3.7 minutes. You wish to test this claim at the 0.05 level of significance. The mean waiting
time for a random sample of n = 85 customers is 3.3 minutes with a sd of 0.8 minutes. Compute the
value of the test statistic.
8. The National Weather Service says that the mean daily high temperature for October in a large
Midwestern city is 56° F. A local weather service wants to test the claim of 56° because it believes
it is lower. A sample of mean daily high temps for October over the past 31 years yields x-bar = 54
with s = 5.6. Test the NWS claim using the “Classical Method” at the .05 sig. level.
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Math 1530 Chapter 7 Review Questions

  1. Write the null and alternative hypotheses for the following: A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz.

2a. Assume that the data has a normal distribution and sigma (σ) is not known. The sample size is

  1. Find the critical t value for:

2a. Right tail test, α = 0.1. (Hint: Use Table A-3)

2b. Left tail test, α = 0.05.

2c. Two tailed test, α = 0.

  1. Find the test statistic for the following situations:

a. The claim is that the mean is 0.21; the sample statistics include: n = 32; x-bar = 0.83, s = 0.24.

b. The claim is that the mean < 1.39; sample stats include: n = 87; x-bar = 0.83; s = 0.16.

c. The claim is that the mean is at least 50; sample stats include: n = 100; x-bar = 54.8; s = 3.

  1. An entomologist writes an article in a scientific journal which claims that fewer than 7 in 10, (0.0007) male fireflies are unable to produce light due to a genetic mutation. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to REJECT the null hypothesis, state the conclusion in non-technical terms. A. There is sufficient evidence to support the claim that the true proportion is greater than . B. There is not sufficient evidence to support the claim that the true proportion is less than . C. There is not sufficient evidence to support the claim that the true proportion is greater than . D. There is sufficient evidence to support the claim that the true proportion is less than .0007.
  2. Suppose you wish to use a hypothesis test to test a claim made by a juice bottling company regarding the mean amount of juice in its 16 oz bottles. Why does the original claim sometimes become the null hypothesis, and why does it sometimes become the alternative hypothesis. Give examples.
  3. A store manager claims that the mean amount of time customers spend waiting in line is less than 3.7 minutes. You wish to test this claim at the 0.05 level of significance. The mean waiting time for a random sample of n = 85 customers is 3.3 minutes with a sd of 0.8 minutes. Compute the value of the test statistic.
  4. The National Weather Service says that the mean daily high temperature for October in a large Midwestern city is 56° F. A local weather service wants to test the claim of 56° because it believes it is lower. A sample of mean daily high temps for October over the past 31 years yields x-bar = 54 with s = 5.6. Test the NWS claim using the “Classical Method” at the .05 sig. level.
  1. A researcher wants the test the claim that among car owners in a particular town, the mean number of miles driven per year is greater than 14,000 miles. He randomly selects 26 drivers and finds that this sample drives an average of 18,180 miles with a s.d. of 10,348 miles. Test the claim at the 0.01 level.
  2. An educational testing company has been using a standard test of verbal ability and the mean has been 430. In analyzing a new version of that test, it is found that a sample of 100 randomly selected subjects produces a mean and s.d. of 412 and 155 respectively. At the 0.05 level of confidence, test the claim using any method that the new version has a mean equal to the past version.
  3. A drug company claims that the side effects of its new drug, Planzap , will be experienced by fewer than 20% of the patients who take the drug. In a clinical trial, 68 of 400 subjects experienced the side effects. Test the company’s claim at the  = 0.01 level.
  4. A nationwide study of American homeowners revealed (claimed) that 64% have one or more lawn mowers. A lawn equipment manufacturer, located in Omaha, feels the estimate is too low for households in Omaha. The manufacturer’s survey of 498 homes in Omaha yielded 332 with one or more lawn mowers? Test the claim using α = 0.05.

Chapter 9:

The following data represent the gestation period of various animals along with their life expectancy. A zoologist would like to determine if he could use gestation/incubation time to predict the life expectancy of the animal.

Animal Gestation Period (days) (x)

Life Expectancy (yrs)

Animal Gestation Period (days) (x)

Life Expectancy (yrs)

Cat 63 11 Chicken 22 7. Dog 63 11 Duck 28 10 Goat 151 12 Lion 108 10 Parakeet 18 8 Pig 115 10 Rabbit 31 7 Squirrel 44 9 Source: Time Almanac 2000

a. Find the value of the linear correlation coefficient r. b. How would you describe this relationship? (in terms of strength and direction) c. Give the coefficient of determination (r^2 )and d. explain its meaning. (Write the sentence: “____% of the variation in ……….” e. Write the equation that best models the data (the regression equation). f. Write a description of this equation in context of the data … in terms of “life expectancy” and “gestation period”. g. Use your regression equation to predict the life expectancy of a guinea pig. (Gestation period of a guinea pig is 68 days.)