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#1. Consider the hypothesis test...

#1. Consider the hypothesis test given by

H0: µ = 530

H1: µ ≠ 530

In a random sample of 85 subjects, the sample mean is found to be x = 522.3.Also, the population standard deviation is σ = 29.

Determine the p-value for this test. Is there sufficient evidence to justify the rejection of H 0 at the α = 0.01 level? Explain.

#3. Airline overbooking is a common practice. Due to uncertain plans, many people cancel at the last minute or simply fail to show up. Air Eagle is a small commuter airline. Its past records indicate that 80% of the people who make a reservation will show up for the flight. The other 20% do not show up. Air Eagle decided to book 12 people for today’s flight. Today’s flight has just 10 seats.

Find the probability that there are enough seats for all the passengers who show up. (Hint: Find the probability that in 12 people, 10 or less show up.)

How many passengers are expected to show up?

#3. Consider the following data:

X 0 -2 1 1 2

Y 2 -2 5 4 8

Find an equation of the least squares regression line. Show all work; writing the correct equation, without supporting work, will receive no credit. Also, find the predicted value when x = 1

#4. A certain researcher thinks that the proportion of women favoring stricter gun control is higher than the proportion of men favoring stricter gun control.

In a sample of 360 women, 65% favored stricter gun control laws.

In a random sample of 220 men, 60% favored stricter gun control laws.

At the 0.05 significance level, is there sufficient evidence to support the claim that the proportion of women favoring stricter gun control is higher than the proportion of men favoring stricter gun control? Show all work and justify your answer

#5. Preliminary road tests conducted by the Econotire’s quality control division suggest that the lifetimes of its new, inexpensive radial are normally distributed with mean lifetime of 30,000 miles and standard deviation of 5,000 miles. Your store has just received a shipment of 1,000 such tires.

What is the probability that a randomly selected tire lasts longer than 38,100 miles?

How many tires in your shipment do you expect to last between 27,500 and 33,800 miles?

Find the 94th percentile of this distribution.

#6. According to the manufacturer of M&M candy, the color distribution for plain chocolate M&Ms is 13% brown, 13% red, 14% yellow, 24% blue, 20% orange, and 16% green.

A student found a bag of 350 M&M’s at Costco. Instead of doing her

homework, she sorted the M&M’s in the bag by color. She counted 41 brown, 55 red, 49 yellow, 95 blue, 80 orange, and 30 green M&M’s.

At the 0.01 level, is the distribution of colors of M&M’s different than stated by the

manufacturer? Show all work and justify your answer.

H0: µ = 530

H1: µ ≠ 530

In a random sample of 85 subjects, the sample mean is found to be x = 522.3.Also, the population standard deviation is σ = 29.

Determine the p-value for this test. Is there sufficient evidence to justify the rejection of H 0 at the α = 0.01 level? Explain.

#3. Airline overbooking is a common practice. Due to uncertain plans, many people cancel at the last minute or simply fail to show up. Air Eagle is a small commuter airline. Its past records indicate that 80% of the people who make a reservation will show up for the flight. The other 20% do not show up. Air Eagle decided to book 12 people for today’s flight. Today’s flight has just 10 seats.

Find the probability that there are enough seats for all the passengers who show up. (Hint: Find the probability that in 12 people, 10 or less show up.)

How many passengers are expected to show up?

#3. Consider the following data:

X 0 -2 1 1 2

Y 2 -2 5 4 8

Find an equation of the least squares regression line. Show all work; writing the correct equation, without supporting work, will receive no credit. Also, find the predicted value when x = 1

#4. A certain researcher thinks that the proportion of women favoring stricter gun control is higher than the proportion of men favoring stricter gun control.

In a sample of 360 women, 65% favored stricter gun control laws.

In a random sample of 220 men, 60% favored stricter gun control laws.

At the 0.05 significance level, is there sufficient evidence to support the claim that the proportion of women favoring stricter gun control is higher than the proportion of men favoring stricter gun control? Show all work and justify your answer

#5. Preliminary road tests conducted by the Econotire’s quality control division suggest that the lifetimes of its new, inexpensive radial are normally distributed with mean lifetime of 30,000 miles and standard deviation of 5,000 miles. Your store has just received a shipment of 1,000 such tires.

What is the probability that a randomly selected tire lasts longer than 38,100 miles?

How many tires in your shipment do you expect to last between 27,500 and 33,800 miles?

Find the 94th percentile of this distribution.

#6. According to the manufacturer of M&M candy, the color distribution for plain chocolate M&Ms is 13% brown, 13% red, 14% yellow, 24% blue, 20% orange, and 16% green.

A student found a bag of 350 M&M’s at Costco. Instead of doing her

homework, she sorted the M&M’s in the bag by color. She counted 41 brown, 55 red, 49 yellow, 95 blue, 80 orange, and 30 green M&M’s.

At the 0.01 level, is the distribution of colors of M&M’s different than stated by the

manufacturer? Show all work and justify your answer.

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