# Hypothesis Testing explained in this solution

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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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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.

(a) At the .01 level of significance,is the true mean greater than 10?

Null Hypothesis: Ho: M = 10 :Mean is 10 or less pages

Alternative Hypothesis: H1: M >10 :Mean is more than 10 pages

Significance level=alpha (a) = 0.01 or 1%

No of tails= 1

This is a 1-tailed test because we are testing that the mean is greater than 10

Since sample size= 35 >= 30

we will use normal distribution

This is a one tailed test because we are testing the area in the right tail

Since the sample size is large we will use z distribution

Z at the 0.01 level of significance 1 tailed test = 2.3263

z critical= 2.3263

Decision rule

If the sample z value > z critical, 2.3263 reject Null Hypothesis

If the sample z value < z critical , 2.3263 accept Null Hypothesis

Alternatively:

If p value < significance level , 0.01 reject Null Hypothesis

If p value > significance level , 0.01 accept Null Hypothesis

Hypothesized Mean=M = 10 pages

Standard deviation =s= 4.45 pages

sample size=n= 35

sx=standard error of mean=s/square root of n= 0.7522 = ( 4.45 /square root of 35)

sample mean= 14.44 pages

z=(sample mean-M )/sx= 5.9027 =(14.44-10)/0.7522

Reject Null Hypothesis since z> z critical

The mean is greater than 10 pages

(b) Use Excel to find the right-tail p-value.

Prob-value corresponding to z= 5.9027 is 1.788E-09 (calculated using Excel Function NORMSDIST)

which is less than the significance level of 0.01

Reject Null ...

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