# P Value

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Category: Mathematics > Probability Problems

Subject: Test of Statistical Hypothesis

Details: To whom it may concern,

I need help answering these 4 problems. Please include,

1) all the steps with details on how to arrive at each solution.

2) final solution

I prefer to have everything worked out in MS Word and MS Excel. Thank-you.

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1. A check cashing service found that 5% of all checks submitted to the service were bad. (i.e. they could not be cashed for lack of funds). After instituting a check verification system, a sample of 1124 checks produced only 45 that were bad. Does the evidence exist to affirm that the check verification reduces the probability of bad checks? What p value do you give this test?

2. An experiment to explore pain thresholds to electrical shock for males and females results in the follow data summary:

Males Females

Totals 14 10

Average 16.2 14.9

Variance(s2 ) 12.7 26.4

Does the data provide sufficient evidence that the variance in pain thresholds for men and women are different? Use α = .10

3. Two different methods of training new employees are tested and the times for assembly of the product are noted.

Standard Procedure New Procedure

N1 = 9 N2 = 9

Y1(bar) = 35.22 Y2(bar) = 31.56

∑ I (y1i - y1(bar)2) = 195.56 ∑I (y2i - y2(bar)2) = 160.22

Is there a difference of the true mean times of assembly based on the two methods? Test at α = .05

4. A lab technician wants to compare the breaking strength of three brands of thread. Originally he planned to do more, but he lacked time. The breaking in thread is measured in ounces.

Thread 1 18 16.4 15.7 19.6 16.5 18.2

Thread 2 21.1 17.8 18.6 20.8 17.9 19

Thread 3 16.5 17.8 16.1

Test at α =.05 whether the differences in sample means are significant.

##### Solution Preview

please refer to the attachment.

<br>

<br>

<br>1. A check cashing service found that 5% of all checks submitted to the service were bad. (i.e. they could not be cashed for lack of funds). After instituting a check verification system, a sample of 1124 checks produced only 45 that were bad. Does the evidence exist to affirm that the check verification reduces the probability of bad checks? What p value do you give this test?

<br>

<br>This is a test of proportion.

<br>Ho: Prob(bad checks)=0.05

<br>Ha: Prob(bad checks)<0.05

<br>The sample proportion is q=45/1124=0.04

<br>The sample standard error is:

<br>SE=SQRT(q*(1-q)/n)= SQRT(0.04*(1-0.04)/1124)= 0.00584

<br>Calculate z value by z=(0.05-q)/SE=(0.05-0.04)/ 0.00584=1.71

<br>Then from a z-table, Prob(z<1.71) is 0.9564

<br>the p-value is 1-0.9564 =0.436, which is less than 0.05

<br>therefore, we reject Ho with 0.05 level of significance, and conclude that the check verification reduces the probability of bad checks.

<br>

<br>2. An experiment to explore pain thresholds to electrical shock for males and females results in the follow data summary:

<br>

<br>Males Females

<br>Totals 14 10

<br>Average 16.2 14.9

<br>Variance(s2 ) 12.7 26.4

<br>

<br>Does the data provide sufficient evidence that the variance in pain thresholds for men and women are different? Use α = .10

<br>

<br>Ho: VARm = VARf

<br>H1: VARm <> VARf

<br>We can use a very simple F-test for the variance.

<br>Because the data are assuming to follow a normal distribution, we can take the estimated variances of both groups as unbiased estimates.

<br>Then F=VARf / VARm = 26.4/12.7=2.08

<br>Degree of Freedom1=10-1=9

<br>Degree of Freedom2=14-1=13

<br>From a 0.10 F-table, we find that F*(9,13)=2.16

<br>As F^ < F*, we fail to reject H0 and conclude that the ...

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