# Hypothesis Testing Problems: P-value Method

1. The senior management of the electric power utility company, let there be light (LTBL), has recently built, at considerable expense, a state of the art nuclear power plant in Gary, Indiana. The utility has applied for a start-up permit from the Environmental Protection Agency (EPA), which has expressed concern over the potential threat to the ecology of Lake Michigan posed by the temperature of the waste water from the plant.

In particular, EPA scientists have established that a power plant's cooling system is working properly when the mean temperature of waste water from LTBL's cooling system does not meet the specification, that is, they believe waste water from the LTBL cooling system is, on average, greater than 58 degrees Fahrenheit. EPA technicians have taken a random sample of 81 temperature readings and found a sample mean of 58.46 degrees Fahrenheit. Based on data obtained from similar plants, it is assumed that the population standard deviation is 2 degrees Fahrenheit.

Conduct a hypothesis test. What is the p-value, and how much evidence is there to conclude that the power plant's cooling system is not working properly, i.e. , to reject the null hypothesis Ho: u less than or equal to 58 degrees and accept the alternative hypothesis Ha: u >58 degrees Fahrenheit.

a. P - Value: __________________________

Round your final answer t three decimal places.

b. The weight of evidence that the mean temperature of waste water is greater than 58 degrees Fahrenheit is:_________________________________

a. Some evidence

b. Strong evidence

c. Very Strong evidence

d. Extremely strong evidence

e. Little evidence

f. USE the interpreting the weight of evidence against the null hypothesis to help with part b.

If the p-value for testing Ho is less than:

.10, we have some evidence that Ho is false.

.05, we have strong evidence that Ho is false.

.01, we have very strong evidence that Ho is false.

.001, we have extremely strong evidence that Ho is false.

2. Vendall leases soft drink vending machines that are designed to dispense 10 ounces of soft drink. Customers complain when machines dispense too much soft drink, causing spillage, and customers also complain when machines dispense too little soft drink. A particular machine is being tested by a random sample of 144 soft drinks. The results are x =9.96 oz and, based on historical data on the same model of machine, the population standard deviation o =.36 oz.

Conduct a hypothesis test. What is the p-value, and how much evidence is there to conclude that the vending machine needs adjustment, i.e., to reject null hypothesis Ho:u = 10 oz and accept the alternative hypothesis Ha: u not equal to 10 oz.

a. P- Value:_______________________________

Round your final answer to three decimal places

b. The weight of evidence in support of the conclusion that the vending machine needs adjustment is: ___________________________________

g. Some evidence

h. Strong evidence

i. Very Strong evidence

j. Extremely strong evidence

k. Little evidence

l. USE the interpreting the weight of evidence against the null hypothesis to help with part b.

If the p-value for testing Ho is less than:

.10, we have some evidence that Ho is false.

.05, we have strong evidence that Ho is false.

.01, we have very strong evidence that Ho is false.

.001, we have extremely strong evidence that Ho is false.

3. The Fast Motor Company wishes to estimate the mean dollar amount of damage done to a new model Speedster as a result of a 10 mph crash into the rear bumper of a parked car. 36 Speedsters are test crashed into parked cars and the dollar amount of damage done to each is record. The results from the sample are x = $438 and s = $86.

Conduct a hypothesis test. What is the P-Value, and how much evidence is there that the population mean damage is less than $475, i.e., to reject the null hypothesis Ho: Greater than or equal to $475 and accept the alternative hypothesis Ha: < $475.

a. P- Value:_______________________________

Round your final answer to three decimal places

b. The weight of evidence in support of the alternative hypothesis that the population mean damage is less than $475 is: _________________________________________

m. Some evidence

n. Strong evidence

o. Very Strong evidence

p. Extremely strong evidence

q. Little evidence

r. USE the interpreting the weight of evidence against the null hypothesis to help with part b.

If the p-value for testing Ho is less than:

.10, we have some evidence that Ho is false.

.05, we have strong evidence that Ho is false.

.01, we have very strong evidence that Ho is false.

.001, we have extremely strong evidence that Ho is false.

4. A random sample of 300 beer drinkers is selected and each member of the sample is asked to choose between two brands of beers: Brand A and Brand B. The results are that 165 prefer Brand and 135 prefer Brand B.

Conduct a hypothesis test. What is the p-value, and how much evidence is there to conclude that more than 50% of beer drinkers prefer Brand A over Brand B, i.e., to reject the null hypothesis Ho: P less than or equal to .50 and accept the alternative hypothesis Ha: p > .50.

a. P- Value:_______________________________

Round your final answer to three decimal places

b. The weight of evidence that more than 50% of beer drinkers prefer Brand A over Brand B is: _________________________________________

s. Some evidence

t. Strong evidence

u. Very Strong evidence

v. Extremely strong evidence

w. Little evidence

x. USE the interpreting the weight of evidence against the null hypothesis to help with part b.

.10, we have some evidence that Ho is false.

.05, we have strong evidence that Ho is false.

.01, we have very strong evidence that Ho is false.

.001, we have extremely strong evidence that Ho is false.

https://brainmass.com/statistics/hypothesis-testing/hypothesis-testing-problems-p-value-method-372672

#### Solution Summary

The solution provides step by step method for the calculation of p-values. Formula for the calculation and Interpretations of the results are also included.

Hypothesis Testing Problems Based on the P Value Method and the Traditional Method

9.54 Faced with rising fax costs, a firm issued a guideline that transmissions of 10 pages or more should be sent by 2-day mail instead. Exceptions are allowed, but they want the average to be 10 or below. The firm examined 35 randomly chosen fax transmissions during the next year, yielding a sample mean of 14.44 with a standard deviation of 4.45 pages. (a) At the .01 level of significance, is the true mean greater than 10? (b) Use Excel to find the right-tail p-value

9.56 A coin was flipped 60 times and came up heads 38 times. (a) At the .10 level of significance, is the coin biased toward heads? Show your decision rule and calculations. (b) Calculate a p-value and interpret it.

9.62 The Web-based company Oh Baby! Gifts has a goal of processing 95 percent of its orders on the same day they are received. If 485 out of the next 500 orders are processed on the same day, would this prove that they are exceeding their goal, using alpha = .025? (See story.news.yahoo.com accessed June 25, 2004.)

9.64 An auditor reviewed 25 oral surgery insurance claims from a particular surgical office, determining that the mean out-of-pocket patient billing above the reimbursed amount was $275.66 with a standard deviation of $78.11. (a) At the 5 percent level of significance, does this sample prove a violation of the guideline that the average patient should pay no more than $250 out-of-pocket? State your hypotheses and decision rule. (b) Is this a close decision?

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