Testing: H0:μ=9.1 Ha:μ<9.1 Your sample consists of 23 subjects, with a mean of 8.9 and standard deviation of 3.77. Calculate the test statistic, rounded to 2 decimal places. t =

1.

Testing:

H0:μ=9.1
Ha:μ<9.1

Your sample consists of 23 subjects, with a mean of 8.9 and standard deviation of 3.77.

Calculate the test statistic, rounded to 2 decimal places. t =

2.

CNNBC recently reported that the mean annual cost of auto insurance is 994 dollars. Assume the standard deviation is 137 dollars. You will use a simple random sample of 117 auto insurance policies.

Find the probability that a single randomly selected policy has a mean value between 985.1 and 1013 dollars.
P(985.1 < X < 1013) = 

Find the probability that a random sample of size n=117 has a mean value between 985.1 and 1013 dollars.
P(985.1 < x < 1013) = 

Enter your answers as numbers accurate to 4 decimal places.

3.

A leading magazine reported at one time that the average number of weeks an individual is unemployed is 18.7 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 18.7 weeks and that the population standard deviation is 9.1 weeks. Suppose you would like to select a random sample of 210 unemployed individuals for a follow-up study.

Find the probability that a single randomly selected value is between 17.6 and 19.
P(17.6 < X < 19) = 

Find the probability that a sample of size n=210 is randomly selected with a mean between 17.6 and 19.
P(17.6 < x < 19) = 

Enter your answers as numbers accurate to 4 decimal places. Answers should be obtained using z-scores rounded to two decimal places.

4. 

A population of values has a normal distribution with μ=151.5 and σ=75.8. You intend to draw a random sample of size n=92

Find the probability that a single randomly selected value is between 138.9 and 174.4.
P(138.9 < X < 174.4) = 

Find the probability that a sample of size n=92 is randomly selected with a mean between 138.9 and 174.4.
P(138.9 < x < 174.4) = 

Enter your answers as numbers accurate to 4 decimal places. Answers should be obtained using z-scores correct to two decimal places.

5.

A population of values has a normal distribution with μ=14.8 and σ=6.5 You intend to draw a random sample of size n=131

Find the probability that a single randomly selected value is less than 13.
P(X < 13) = 

Find the probability that a sample of size n=131 is randomly selected with a mean less than 13.
P(x< 13) = 

Enter your answers as numbers accurate to 4 decimal places. Answers should be obtained using z-scores correct to two decimal places. 

6.

A population of values has a normal distribution with μ=48.5 and σ=76.9. You intend to draw a random sample of size n=31

Find the probability that a single randomly selected value is between 5.4 and 32.3.
P(5.4 < X < 32.3) = 

Find the probability that a sample of size n=31 is randomly selected with a mean between 5.4 and 32.3.
P(5.4 < x < 32.3) = 

Enter your answers as numbers accurate to 4 decimal places. Answers should be obtained using z-scores correct to two decimal places.

7.

A population of values has a normal distribution with μ=120.9 and σ=96.2. You intend to draw a random sample of size n=201.

Find the probability that a single randomly selected value is less than 120.6.
P(X < 120.6) = 

Find the probability that a sample of size n=201 is randomly selected with a mean less than 120.6.
P{x < 120.6) = 

Enter your answers as numbers accurate to 4 decimal places. Answers should be obtained using z-scores correct to two decimal places.

8.

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 258.1 cm and a standard deviation of 0.5 cm. For shipment, 14 steel rods are bundled together.

Find the probability that the average length of a randomly selected bundle of steel rods is between 257.8 cm and 258.4 cm.
P(257.8 cm < x < 258.4 cm) = 

Enter your answer as a number accurate to 4 decimal places. Answers should be obtained using z-scores correct to two decimal places.

9.

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 107.1 cm and a standard deviation of 1.2 cm. For shipment, 25 steel rods are bundled together.

Find the probability that the average length of a randomly selected bundle of steel rods is greater than 106.5 cm.
P(x¯ > 106.5 cm) = 

Enter your answer as a number accurate to 4 decimal places. Answers should be obtained using z-scores rounded to two decimal places.

10. You are testing the claim that the proportion of men who own cats is larger than the proportion of women who own cats.

You sample 50 men, and 65% own cats.

You sample 90 women, and 50% own cats.

Find p¯ (p-bar), as a decimal, rounded to two decimal places.