Calculus and Above

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Refer to the following information...

Refer to the following information for Questions 23, 24, and 25.

The IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.

23.What is the probability that a randomly person has an IQ between 85 and 115?

24.Find the 90th percentile of the IQ distribution.

25.If a random sample of 100 people is selected, what is the standard deviation of the sample mean?

26.Consider the hypothesis test given by

H0∶ µ=530

H1∶ µ≠530

In a random sample of 81 subjects, the sample mean is found to be 524.x=Also, the population standard deviation is 27.

Determine the P-value for this test. Is there sufficient evidence to justify the rejection of H_0

at the a=0.01 level? Explain.

27. A certain researcher thinks that the proportion of women who say that the earth is getting warmer is greater than the proportion of men.

In a random sample of 250 women, 70% said that the earth is getting warmer.

In a random sample of 220 men, 67% said that the earth is getting warmer.

At the 0.05 significance level, is there sufficient evidence to support the claim that the proportion of women saying the earth is getting warmer is higher than the proportion of men saying the earth is getting warmer? Show all work and justify your answer.

Refer to the following data for Questions 28 and 29.

x 0 – 1 1 2 3

y 3 – 2 6 4 7

28. Is there a linear correlation between x and y at the 0.05 significance level? Justify your answer.

29. Find an equation of the least squares regression line. Show all work; writing the correct equation, without supporting work, will receive no credit.

30. The Daily News reported that the color distribution for plain M&M’s was: 40% brown, 20% yellow, 20% orange, 10% green, and 10% tan. Each piece of candy in a random sample of 100 plain M&M’s was classified according to color, and the results are listed below. Use a 0.05 significance level to test the claim that the published color distribution is correct. Show all work and justify your answer.

Color Brown Yellow Orange Green Tan

Number 42 21 12 7 18

The IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.

23.What is the probability that a randomly person has an IQ between 85 and 115?

24.Find the 90th percentile of the IQ distribution.

25.If a random sample of 100 people is selected, what is the standard deviation of the sample mean?

26.Consider the hypothesis test given by

H0∶ µ=530

H1∶ µ≠530

In a random sample of 81 subjects, the sample mean is found to be 524.x=Also, the population standard deviation is 27.

Determine the P-value for this test. Is there sufficient evidence to justify the rejection of H_0

at the a=0.01 level? Explain.

27. A certain researcher thinks that the proportion of women who say that the earth is getting warmer is greater than the proportion of men.

In a random sample of 250 women, 70% said that the earth is getting warmer.

In a random sample of 220 men, 67% said that the earth is getting warmer.

At the 0.05 significance level, is there sufficient evidence to support the claim that the proportion of women saying the earth is getting warmer is higher than the proportion of men saying the earth is getting warmer? Show all work and justify your answer.

Refer to the following data for Questions 28 and 29.

x 0 – 1 1 2 3

y 3 – 2 6 4 7

28. Is there a linear correlation between x and y at the 0.05 significance level? Justify your answer.

29. Find an equation of the least squares regression line. Show all work; writing the correct equation, without supporting work, will receive no credit.

30. The Daily News reported that the color distribution for plain M&M’s was: 40% brown, 20% yellow, 20% orange, 10% green, and 10% tan. Each piece of candy in a random sample of 100 plain M&M’s was classified according to color, and the results are listed below. Use a 0.05 significance level to test the claim that the published color distribution is correct. Show all work and justify your answer.

Color Brown Yellow Orange Green Tan

Number 42 21 12 7 18

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