# Probability and hypothesis testing problems

1. A manufacturing company measures the weight of boxes before shipping them to the customers. If the box weights have a population mean and standard deviation of 90 lbs. and 24 lbs. respectively, then based on a sample size of 36 boxes, the probability that the average weight of the boxes will:

Be less than 84 lbs. is:

a. 16.87%

b. 93.32%

c. 43.32%

d. 6.678%

e. 84.13%

2. In a manufacturing process a machine produces bolts that have an average length of 3 inches with a variance of .03. If we randomly select three bolts from this process:

What is the standard deviation of the sample mean?

a. 0.03

b. 0.01

c. 0.1732

d. 0.0577

e. 0.10

3. In a manufacturing process a machine produces bolts that have an average length of 3 inches with a variance of .03. If we randomly select three bolts from this process:

What is the probability the mean length of the bolt is at least 3.16 inches?

a. 97.72%

b. 5.48%

c. 94.52%

d. 44.52%

e. 2.28%

4. In a manufacturing process a random sample of 36 bolts manufactured has a mean length of 3 inches with a standard deviation of .3 inches. What is the 99% confidence interval for the true mean length of the bolt?

a. 2.902 to 3.098

b. 2.884 to 3.117

c. 2.871 to 3.129

d. 2.228 to 3.772

e. 2.902 to 3.098

5. Health insurers and the federal government are both putting pressure on hospitals to shorten the average length of stay (LOS) of their patients. In 1996, the average LOS for non-heart patient was 4.6 days. A random sample of 20 hospitals in one state had a mean LOS for non-heart patients in 2000 of 3.8 days and a standard deviation of 1.2 days.

Calculate a 95% confidence interval for the population mean LOS for non-heart patients in the state's hospitals in 2000.

a.[3.24 - 4.36]

b.[3.67 - 3.93]

c.[3.34 - 4.26]

d.[3.38 - 4.22]

e.[3.27 - 4.33]

6. If a null hypothesis is rejected at a significance level of .05, it will ______ be rejected at a significance level of .01

a. Always

b. Sometimes

c. Never

7. For the following hypothesis test where H0: μ ≤? 10 vs. Ha: μ > 10, we reject H0 at level of significance α and conclude that the true mean is greater than 10 when the true mean is really 14. Based on this information we can state that we have:

a. Made a Type I error

b. Made a Type II error

c. Made a correct decision

d. Increased the power of the test

8. The average waiting time per customer at a fast food restaurant has been 7.5 minutes. The customer waiting time has a normal distribution. The manager claims that the use of a new cashier system will decrease the average customer waiting time in the store.

A random sample of 12 customer transactions has been recorded. At a significance level of .05, what is the rejection point condition? We would reject the null hypothesis if:

a. Z < -1.645

b. Z > 1.645

c. t > 1.796

d. t < -1.796

e. t < -1.782

9. A major airline company is concerned that its proportion of late arrivals has substantially increased in the past month. Historical data shows that on the average 18% of the company airplanes have arrived late. In a random sample of 1,240 airplanes, 310 airplanes have arrived late. If we are conducting a hypothesis test of a single proportion to determine if the proportion of late arrivals has increased:

What is the correct statement of null and alternative hypothesis?

a. H0: p < .18 and HA: p ≥ .18

b. H0: p ≤ .18 and HA: p > .18

c. H0: p = .18 and HA: p ≠ .18

d. H0: p > .18 and HA: p ≤ .18

e. H0: p ≤ .20 and HA: p > .20

10. A study investigated the relationship of employment status to mental health. A sample of 49 unemployed men took a mental health examination measuring present mental health with lower values indicating better mental health. Their mean score was 10.94 and a standard deviation of 4.90.

Calculate the p-value for the test statistic.

a. 0.0901

b. 0.0037

c. 0.0015

d. -0.0015

e. -0.0901

#### Solution Summary

The solution provides step by step method for the calculation of problems from probability and hypothesis testing. Formula for the calculation and Interpretations of the results are also included.