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# Hypothesis Testing Problems: P-value Method

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1. Since 9/11/2001, there has been increased concern for passenger safety. This has led to calls for new and more intrusive passenger screening equipment. While concerns for passengers' privacy are an important part of the debate, there are also concerns for the length of time required to move passengers through the proposed new screening devices, and the strain on travelers caused by additional delays.

The manufacturer of the proposed new scanning device claims that individual passengers can move through in less than 5 seconds on average. A random sample of 100 passengers is put through the new machine and the sample mean time is found to be 4.86 seconds. Based on earlier tests of a similar machine installed in a foreign airport, the population standard deviation is known to be .48 seconds.

Conduct a hypothesis test; find the p-value; and interpret the weight of evidence provided by the p-value in support of the manufacturer's claim, i.e., to reject the null hypothesis Ho: u greater than or equal to 5 seconds and accept the alternative hypothesis Ha: u < 5 seconds.

a. P - Value: __________________________

b. The weight of evidence to conclude that the manufacturer's claim is correct 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. Ralph's manufacturing produces small wheels that should have a mean diameter of 4 inches. A random sample of 100 wheel diameters yielded a sample mean x=3.93 inches. Based on historical data on machines of this type, a population standard deviation of 0=.30inches can be used for this test.

Conduct a hypothesis test. What is the p-value, and how much evidence is there to conclude that the lot of wheels from which the sample was chosen fails to have a population mean of 4 inches, i.e., to reject the null hypothesis Ho: u = 4 inches and accept the alternative hypothesis Ha: u not equal 4 inches.

a. P- value:_________________________________________

b. The weight of evidence in support of the alternative hypothesis that the lot of wheels from which the sample was chosen fails to have a population mean of 4 inches 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. A manufacturer of athletic footwear claims that the mean useful lifetime of his product will exceed 50 hours. A random sample of 36 pairs of shoes leads to the following sample results, in terms of useful life: x=52.3 hours and s = 9.6 hours.

Conduct a hypothesis test. What is the p-value, and how much evidence is there to conclude that the manufacturer's claim is correct, i.e., to reject the null hypothesis Ho: u less than or equal to 50 hours and accept the alternative hypothesis Ha: u > 50 hours

a. P- value:_________________________________________

b. The weight of evidence to conclude that the manufacturer's claim is correct: _________________________________
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. Residents living near the smelting plant located just outside your town have complained that the plant violates the town's noise pollution code. The code states that to be in compliance, noise levels are allowed to exceed 120 decibels less than 10% of the time. A community action group, to which you belong, has been monitoring the noise level at randomly selected times. The group took 150 sound level readings and found 11 above 120 decibels.

Conduct a hypothesis test using MegaStat. Be sure to enter into MegaStat the actual observed values provided in the problem.

What is the p-value, and how much evidence is there to conclude that the plant is in compliance with the noise pollution code, i.e., to reject the null hypothesis Ho: p greater than or equal to .10 and accept the alternative hypothesis Ha: p < .10?

a. P- value:_________________________________________

b. The weight of evidence to conclude that the plant is in compliance with the noise pollution code is _________________________________
c. Some evidence
d. Strong evidence
e. Very Strong evidence
f. Extremely strong evidence
g. Little evidence
h. 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.

https://brainmass.com/statistics/hypothesis-testing/hypothesis-testing-problems-p-value-method-372746

#### 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.

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## 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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