# Module 7 and exam 7

*label*Mathematics

*timer*Asked: Dec 17th, 2018

*account_balance_wallet*$35

**Question description**

# Problem Set 7.1

**Problem Set 7.1**

1. In a certain suburb, the mean house price in 2009 was $ 225,000. A real estate agent believes that the mean house price in that suburb has increased since 2009. Please state the null and alternative hypothesis.

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2. According to babycenter.com, the mean height of a six year old boy is 42 inches. A school counselor believes that the mean height of the six year old boys in her school is less than 42 inches. Please state the null and alternative hypothesis.

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3. In 2012, it was reported that McDonald’s had 62 million customers per day. A researcher believes that the number of McDonald’s customers per day is different now. Please state the null and alternative hypothesis.

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4. A lettuce grower claims that the mean weight of her heads of lettuce is 2 pounds. You believe that the mean weight of the lettuce is less than two pounds. Please state the null and alternative hypothesis.

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5. According to Time magazine, in April 2014 the average gas price in the U.S. was $ 3.70. A financial analyst believes that the average gas price is different today. Please state the null and alternative hypothesis.

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6. According to the wall street journal, in 2011 the average (or mean) cable bill was $ 128 per month. You believe that the mean cable bill is higher today. Please state the null and alternative hypothesis.

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# Problem Set 7.2

**Problem Set 7.2**

(These problems are the same as problem set 7.1 except now you are being asked to state what it means to make Type I and Type II errors.)

1. In a certain suburb, the mean house price in 2009 was $ 225,000. A real estate agent believes that the mean house price in that suburb has increased since 2009.

a) Explain what it would mean to make a Type I error.

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b) Explain what it would mean to make a Type II error.

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2. According to babycenter.com, the mean height of a six year old boy is 42 inches. A school counselor believes that the mean height of the six year old boys in her school is less than 42 inches. Please state the null and alternative hypothesis.

a) Explain what it would mean to make a Type I error.

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b) Explain what it would mean to make a Type II error.

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3. In 2012, it was reported that McDonald’s had 62 million customers per day. A researcher believes that the number of McDonald’s customers per day is different now. Please state the null and alternative hypothesis.

a) Explain what it would mean to make a Type I error.

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b) Explain what it would mean to make a Type II error.

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4. A lettuce grower claims that the mean weight of her heads of lettuce is 2 pounds. You believe that the mean weight of the lettuce is less than two pounds. Please state the null and alternative hypothesis.

a) Explain what it would mean to make a Type I error.

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b) Explain what it would mean to make a Type II error.

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5. According to Time magazine, in April 2014 the average gas price in the U.S. was $ 3.70. A financial analyst believes that the average gas price is different today. Please state the null and alternative hypothesis.

a) Explain what it would mean to make a Type I error.

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b) Explain what it would mean to make a Type II error.

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6. According to the wall street journal, in 2011 the average (or mean) cable bill was $ 128 per month. You believe that the mean cable bill is higher today. Please state the null and alternative hypothesis.

a) Explain what it would mean to make a Type I error.

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b) Explain what it would mean to make a Type II error.

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# Problem Set 7.3

**Problem Set 7.3**

1. Suppose that we have a problem for which the null and alternative hypothesis are given by:

H_{0}: μ = 660.

H_{1}:μ > 660.

Is this a right-tailed test, left-tailed test, or two-tailed test. Find the z value based on a level of significance of α=.05.

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2. Suppose that we have a problem for which the null and alternative hypothesis are given by:

H_{0}: μ = 890.

H_{1}:μ ≠ 890.

Is this a right-tailed test, left-tailed test, or two-tailed test. Find the z value based on a level of significance of α=.09.

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3. Suppose that we have a problem for which the null and alternative hypothesis are given by:

H_{0}: **μ **= 88.5 ounces.

H_{1}:**μ** **<** 88.5 ounces.

Is this a right-tailed test, left-tailed test, or two-tailed test. Find the z value based on a level of significance of α=.10.

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4. Suppose that we have a problem for which the null and alternative hypothesis are given by:

H_{0}: **μ **= 125 days.

H_{1}: **μ <** 125 days.

Is this a right-tailed test, left-tailed test, or two-tailed test. Find the z value based on a level of significance of α=.02.

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5. Suppose that we have a problem for which the null and alternative hypothesis are given by:

H_{0}: **μ **= 63.8** **minutes.

H_{1}: **μ **> 63.8 minutes.

Is this a right-tailed test, left-tailed test, or two-tailed test. Find the z value based on a level of significance of α=.07.

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6. Suppose that we have a problem for which the null and alternative hypothesis are given by:

H_{0}: **μ **= $1250.

H_{1}:**μ** ≠ $ 1250

Is this a right-tailed test, left-tailed test, or two-tailed test. Find the z value based on a level of significance of α=.12.

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# Problem Set 7.4

**Problem Set 7.4**

1. According to the New York Daily News, March 5, 2014, people 65 years and older watch an average of 50.5 hours of TV per week. We will estimate the standard deviation to be 12.7 hours per week. Your town has many social programs for senior citizens which may reduce the amount of TV that older people watch. You want to find out if it is true that people 65 and older in your town watch less than 50.5 hours of TV per week. So, you sample 40 people 65 and older in your town. You find that the average time that the 40 people watch per week is 45.8 hours. Can the claim be supported to a level of significance of α = .02, test the hypothesis?

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2. In a certain large city the mean birth weight of babies is 7.1 pounds with a standard deviation of 1.2 pounds. You believe that in one neighborhood in the city the mean birth weight is different from 7.1 pounds. You sample 95 births and find the mean weight of the sample to be 7.4 pounds. Can the claim be supported to a level of significance of α = .05, test the hypothesis?

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# Problem Set 7.5

**Problem Set 7.5**

1.A social worker in a certain city claimed that only 25% of the children between 19 and 35 months had not had all of their vaccines. You believe the percentage is higher. In order to test the social worker’s claim, you contact 145 families that have a child between 19 and 35 months and find that 44 of the children had not had all of their vaccines. Can the social worker’s claim be supported to a level of significance of α = .02, test the hypothesis.

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2. A trucking company claims that when it ships eggs, 93% of the eggs will arrive unbroken. You check 350 of the eggs that the trucking company shipped and found that 315 eggs were unbroken. Can the trucking company’s claim be supported to a level of significance of α = .03, test the hypothesis.

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