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In exercise 8 and 10...

In exercise 8 and 10, conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion.

Section 11-2: 8

Flat Tire and Missed Class- A classic story involves four carpooling students who missed a test and gave as an excuse a flat tire. On the makeup test, the instructor asked the students to identify the particular tire that went flat. If they really didn’t have a flat tire, would they be able to identify the same tire that went flat? The author asked 41 other students to identify the tire they would select. The results are listed in the following table (except for one student who selected the spare). Use a 0.05 significance level to test the author’s claim that the results fit a uniform distribution. What does the result suggest about the ability of the four students to select the same tire when they really didn’t have a flat?

Left Front=11, Right Front=15, Left Rear= 8, Right Rear=6

Section 11-2:10 (WT)

Baseball Player Births- In his book outliners, author Malcolm Gladwell argues that more baseball players have birthdates in the months immediately following July 31, because that was the cutoff date for non-school baseball leagues. Here is a sample of frequency counts of months of birthdates of American-born major league baseball players starting with January: 387, 329, 366, 344, 336, 313, 313, 503, 421, 434, 398, and 371. Using a 0.05 significance level, is there sufficient evidence to warrant rejection of the claim that American born major league baseball players are born in different months with the same frequency? Do the sample values appear to support Gladwell’s claim?

Section 12-2: 14

Popular Tree Weights- Weights (kg) of popular trees were obtained from trees planted in a sandy and dry region. The trees were given different treatments identified in a table below. The data are from a study conducted by researchers at Pennsylvania State University and were provided by Minitab, Inc. Use a 0.05 significance level to test the claim that the four treatment categories yield popular trees with the same mean weight. Is there a treatment that appears to be most effective in the sandy and dry region?

No Treatment= 1.21, 0.57, 0.56, 0.13, 1.30

Fertilizer= 0.94, 0.87, 0.46, 0.58, 1.03

Irrigation= 0.07, 0.66, 0.10, 0.82, 0.94

Fertilizer and irrigation= 0.85, 1.78, 1.47, 2.25, 1.64

1. Rhino viruses typically cause common colds. In a test of effectiveness of Echinacea, 42 of the subjects treated with Echinacea developed rhinovirus infections. In a placebo group, 93 of the 109 subjects developed rhino virus infections. Use a 0.05 significance level to test the claim that Echinacea has an effect on rhinovirus infections.

Identify the test statistic. Z=___(Round to two decimal places as needed)

Identify the p value?

2. Listed below are ages of actresses and actors at the time that they won an award for the categories of Best Actress and best Actor. Use the sample data to test for a difference between the ages of actresses and actors when they win the award. Use a 0.05 significance level. Assume that paired sample data is a simple random sample and that the differences have a distribution that is approximately normal.

Actress’s age=20,27,20,59,31

Actor’s= age= 45, 40, 63, 50, 42

T=__(Round to two decimal places as needed)

P-value= (Round to three decimal places as needed)

3. The data below are yields for two different types of corn seed that were used on adjacent plots of land. Assume that the data are simple random samples and that the differences have a distribution that is approximately normal. Construct a 95% confidence interval estimate between type 1 and type 2 yields. What does the confidence interval suggest about farmer Joe’s claim that type 1 seed is better than type 2 seed?

Type 1=, 2032, 2000, 2117, 2602, 2102, 1910, 2271, 1441

Type 2= 2021, 1986, 2096, 2484, 2126, 1948, 2165, 1417

In this example µ_dis the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the type 1 seed yield minus the type 2 seed yield.

The 95% confidence interval is ___ < µ_d<___ (Round to two decimal places as needed)

Section 11-2: 8

Flat Tire and Missed Class- A classic story involves four carpooling students who missed a test and gave as an excuse a flat tire. On the makeup test, the instructor asked the students to identify the particular tire that went flat. If they really didn’t have a flat tire, would they be able to identify the same tire that went flat? The author asked 41 other students to identify the tire they would select. The results are listed in the following table (except for one student who selected the spare). Use a 0.05 significance level to test the author’s claim that the results fit a uniform distribution. What does the result suggest about the ability of the four students to select the same tire when they really didn’t have a flat?

Left Front=11, Right Front=15, Left Rear= 8, Right Rear=6

Section 11-2:10 (WT)

Baseball Player Births- In his book outliners, author Malcolm Gladwell argues that more baseball players have birthdates in the months immediately following July 31, because that was the cutoff date for non-school baseball leagues. Here is a sample of frequency counts of months of birthdates of American-born major league baseball players starting with January: 387, 329, 366, 344, 336, 313, 313, 503, 421, 434, 398, and 371. Using a 0.05 significance level, is there sufficient evidence to warrant rejection of the claim that American born major league baseball players are born in different months with the same frequency? Do the sample values appear to support Gladwell’s claim?

Section 12-2: 14

Popular Tree Weights- Weights (kg) of popular trees were obtained from trees planted in a sandy and dry region. The trees were given different treatments identified in a table below. The data are from a study conducted by researchers at Pennsylvania State University and were provided by Minitab, Inc. Use a 0.05 significance level to test the claim that the four treatment categories yield popular trees with the same mean weight. Is there a treatment that appears to be most effective in the sandy and dry region?

No Treatment= 1.21, 0.57, 0.56, 0.13, 1.30

Fertilizer= 0.94, 0.87, 0.46, 0.58, 1.03

Irrigation= 0.07, 0.66, 0.10, 0.82, 0.94

Fertilizer and irrigation= 0.85, 1.78, 1.47, 2.25, 1.64

1. Rhino viruses typically cause common colds. In a test of effectiveness of Echinacea, 42 of the subjects treated with Echinacea developed rhinovirus infections. In a placebo group, 93 of the 109 subjects developed rhino virus infections. Use a 0.05 significance level to test the claim that Echinacea has an effect on rhinovirus infections.

Identify the test statistic. Z=___(Round to two decimal places as needed)

Identify the p value?

2. Listed below are ages of actresses and actors at the time that they won an award for the categories of Best Actress and best Actor. Use the sample data to test for a difference between the ages of actresses and actors when they win the award. Use a 0.05 significance level. Assume that paired sample data is a simple random sample and that the differences have a distribution that is approximately normal.

Actress’s age=20,27,20,59,31

Actor’s= age= 45, 40, 63, 50, 42

T=__(Round to two decimal places as needed)

P-value= (Round to three decimal places as needed)

3. The data below are yields for two different types of corn seed that were used on adjacent plots of land. Assume that the data are simple random samples and that the differences have a distribution that is approximately normal. Construct a 95% confidence interval estimate between type 1 and type 2 yields. What does the confidence interval suggest about farmer Joe’s claim that type 1 seed is better than type 2 seed?

Type 1=, 2032, 2000, 2117, 2602, 2102, 1910, 2271, 1441

Type 2= 2021, 1986, 2096, 2484, 2126, 1948, 2165, 1417

In this example µ_dis the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the type 1 seed yield minus the type 2 seed yield.

The 95% confidence interval is ___ < µ_d<___ (Round to two decimal places as needed)

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