2 population w/Means

Based on information collected from Census at School surveys, the heights of high school seniors living in Hawaii are approximately normally distributed with mean µ1 = 163.8 cm and standard deviation σ 1 = 22.7 cm. The heights of high school seniors living in Texas are approximately normally distributed with mean µ 2 = 167.1 cm and standard deviation σ 2 = 11.2 cm. Suppose we take separate SRSs of 20 Hawaiian seniors and 25 Texan seniors and measure their heights. Let x-bar-1 − x-bar-2 be the difference in the sample mean heights.

What is the shape of the sampling distribution of µ1 − µ 2 ?

• left skewed

• Approximately normal because both population distributions are approximately normal.

• right skewed

• uniform

Based on information collected from Census at School surveys, the heights of high school seniors living in Hawaii are approximately normally distributed with mean µ1 = 163.8 cm and standard deviation σ 1 = 22.7 cm. The heights of high school seniors living in Texas are approximately normally distributed with mean µ 2 = 167.1 cm and standard deviation σ 2 = 11.2 cm. Suppose we take separate SRSs of 20 Hawaiian seniors and 25 Texan seniors and measure their heights. Let x-bar-1 − x-bar-2 be the difference in the sample mean heights.

What is the mean of the sampling distribution of µ1 − µ 2 ?

• -3.3

• 1.8

• 3.7

• 4.9

Tags

CCSS.6.SP.A.2

Based on information collected from Census at School surveys, the heights of high school seniors living in Hawaii are approximately normally distributed with mean µ1 = 163.8 cm and standard deviation σ 1 = 22.7 cm. The heights of high school seniors living in Texas are approximately normally distributed with mean µ 2 = 167.1 cm and standard deviation σ 2 = 11.2 cm. Suppose we take separate SRSs of 20 Hawaiian seniors and 25 Texan seniors and measure their heights. Let x-bar-1 − x-bar-2 be the difference in the sample mean heights.

What is the standard deviation of the sampling distribution of µ1 − µ 2 ?

• 10.89

• 2.223

• 7.231

• 5.548

Courtney wants to know if name-brand chocolate cookies contain more chocolate chips than the store-brand chocolate cookies. She selects a random sample of 120 name-brand cookies and counts the number of chocolate chips. She finds the mean number of chocolate chips is 18.54 with a standard deviation of 2.71. She does the same with 100 randomly selected store-brand chocolate chip cookies and finds they have a mean of 19.28 chips and a standard deviation of 2.89. Do these data provide convincing evidence at the α = 0.05 significance level of a difference in the average number of chocolate chips in name brand cookies and store-brand cookies?

What are appropriate hypotheses for this example?

• Ho: µ1 − µ 2 = 0

  Ha: µ1 − µ 2 ≠ 0

• Ho: µ1 − µ 2 ≠ 0

  Ha: µ1 − µ 2 > 0

• Ho: µ1 − µ 2 = 0

  Ha: µ1 − µ 2 > 0

• Ho: µ1 − µ 2 = 0

  Ha: µ1 − µ 2 < 0

Courtney wants to know if name-brand chocolate cookies contain more chocolate chips than the store-brand chocolate cookies. She selects a random sample of 120 name-brand cookies and counts the number of chocolate chips. She finds the mean number of chocolate chips is 18.54 with a standard deviation of 2.71. She does the same with 100 randomly selected store-brand chocolate chip cookies and finds they have a mean of 19.28 chips and a standard deviation of 2.89. Do these data provide convincing evidence at the α = 0.05 significance level of a difference in the average number of chocolate chips in name brand cookies and store-brand cookies?

Can we do a hypothesis test with this example?

• No, the sampling isn't random

• No, the samples aren't large enough

• No, the samples are too small

• Yes, all conditions are met.

Tags

CCSS.HSS.IC.B.4

Courtney wants to know if name-brand chocolate cookies contain more chocolate chips than the store-brand chocolate cookies. She selects a random sample of 120 name-brand cookies and counts the number of chocolate chips. She finds the mean number of chocolate chips is 18.54 with a standard deviation of 2.71. She does the same with 100 randomly selected store-brand chocolate chip cookies and finds they have a mean of 19.28 chips and a standard deviation of 2.89. Do these data provide convincing evidence at the α = 0.05 significance level of a difference in the average number of chocolate chips in name brand cookies and store-brand cookies?

What is the t-score and P-value for this problem?

• t = -1.95

  P = .11

• t = 1.95

  P = .11

• t = -1.95

  P = .054

• t = 1.95

  P = .054

Tags

CCSS.HSS.IC.B.4

Courtney wants to know if name-brand chocolate cookies contain more chocolate chips than the store-brand chocolate cookies. She selects a random sample of 120 name-brand cookies and counts the number of chocolate chips. She finds the mean number of chocolate chips is 18.54 with a standard deviation of 2.71. She does the same with 100 randomly selected store-brand chocolate chip cookies and finds they have a mean of 19.28 chips and a standard deviation of 2.89.

Do these data provide convincing evidence at the α = 0.05 significance level of a difference in the average number of chocolate chips in name brand cookies and store-brand cookies?

• Because the P-value = 0.054 is greater than .05 , we reject H0. We have convincing evidence that there is a difference in the average number of chocolate chips in name-brand cookies and the average number of chocolate chips in store-brand cookies.

• Because the P-value = 0.024 is less than .05 , we fail to reject H0. We do not have convincing evidence that there is a difference in the average number of chocolate chips in name-brand cookies and the average number of chocolate chips in store-brand cookies.

• Because the P-value = 0.024 is less than .05 , we reject H0. We have convincing evidence that there is a difference in the average number of chocolate chips in name-brand cookies and the average number of chocolate chips in store-brand cookies.

• Because the P-value = 0.054 is greater than .05, we fail to reject H0. We do not have convincing evidence that there is a difference in the average number of chocolate chips in name-brand cookies and the average number of chocolate chips in store-brand cookies.

Tags

CCSS.HSS.IC.B.4

Do students participating in extracurricular activities have higher grade point averages? In a large national study, a random sample of 455 students who participated in extracurricular activities had a mean GPA of 2.76 with a standard deviation of 0.68. A random sample of 569 students who did not participate in extracurricular activities had a mean GPA of 2.58 with a standard deviation of 0.84.

Construct a 90% confidence interval for the difference in mean grade point averages for students who participate in extracurricular activities and those who do not.

• (0.244, 0.639)

• (0.101, 0.259)

• (0.077, 0.421)

• (0.563, 0.997)

Tags

CCSS.HSS.IC.B.4

Do students participating in extracurricular activities have higher grade point averages? In a large national study, a random sample of 455 students who participated in extracurricular activities had a mean GPA of 2.76 with a standard deviation of 0.68. A random sample of 569 students who did not participate in extracurricular activities had a mean GPA of 2.58 with a standard deviation of 0.84.

Interpret a 90% confidence interval for the difference in mean grade point averages for students who participate in extracurricular activities and those who do not.

• We are 90% confident that the interval from 0.101 to 0.259 captures the true difference in mean GPA of students who do and do not participate in extracurricular activities. The interval suggests that the mean GPA of students who participate in extracurricular activities is between 0.101 and 0.259 greater than the mean GPA of students who do not participate in extracurricular activities.

• We are 90% confident that the interval from 0.101 to 0.259 captures the true difference in mean GPA of students who do and do not participate in extracurricular activities. The interval suggests that the mean GPA of students who do not participate in extracurricular activities is between 0.101 and 0.259 greater than the mean GPA of students who do participate in extracurricular activities.

• We are 90% confident that the true difference in mean GPA of students who do and do not participate in extracurricular activities is positive.

• We are 90% confident that the true difference in mean GPA of students who do and do not participate in extracurricular activities is going to be 2.58.

Tags

CCSS.HSS.IC.B.4

Do students participating in extracurricular activities have higher grade point averages? In a large national study, a random sample of 455 students who participated in extracurricular activities had a mean GPA of 2.76 with a standard deviation of 0.68. A random sample of 569 students who did not participate in extracurricular activities had a mean GPA of 2.58 with a standard deviation of 0.84.

Does this interval provide convincing evidence that there is a difference in mean grade point averages for students who participate in extracurricular activities and those who do not? Explain.

• Because all of the plausible values in the interval (0.101, 0.259) are greater than 0, these data does not provide convincing evidence that the mean GPA of students who participate in extracurricular activities is greater than the mean GPA of students who do not participate in extracurricular activities.

• Because all of the plausible values in the interval (0.101, 0.259) go from negative to positive 0, these data does not provide convincing evidence that the mean GPA of students who participate in extracurricular activities is greater than the mean GPA of students who do not participate in extracurricular activities.

• Because all of the plausible values in the interval (0.101, 0.259) are greater than 0, these data provide convincing evidence that the mean GPA of students who participate in extracurricular activities is greater than the mean GPA of students who do not participate in extracurricular activities.

• Because all of the plausible values in the interval (0.101, 0.259) are less than 0, these data provide convincing evidence that the mean GPA of students who do not participate in extracurricular activities is greater than the mean GPA of students who do participate in extracurricular activities.

Tags

CCSS.HSS.IC.B.4