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# Statistics : 10 Problems

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Use n=25 for each problem where necessary.

An accountant randomly selects (60+n) general accounts payable and examines them to
determine whether they are correct. Six accounts contained errors. Construct a 98% confidence interval for the true proportion of general accounts payable that contain errors.
Compute 95% confidence interval to estimate for the population mean &#956;, if the sample mean x &#773; = 7.4+n , standard deviation &#963; =16 , and n = 100.
Suppose that we want to conduct a poll to estimate the proportion of voters who favor an issue. Assume that 50% of the voters could be in favor of the issue. Find the sample size needed so that we are 99% confidence that the sample proportion of voters who favor the issue is within (0.03+0.01n) of p, the true proportion of all favorers who are in favor of the issue.
Consider a population having a standard deviation equal to 10. We wish to estimate the mean of this population. How large a random sample is needed to make us 90% confident that the sample mean of this population within (3+0.05n) of the true mean.

Use the 5 step procedure for each.

Suppose that a random sample of 16 measurements from a normally distributed population gives a sample mean of x &#773; = (13.5+0.03n) and sample standard deviation s = 6. Test the claim that the mean of all measurements &#956; is greater than 10. That is test the hypothesis H0 : &#956; <10 versus H1:&#956; > 10. Use &#945;= 0.10.

Test the claim that a population mean equals (70+0.04n). You have a sample of 49 items for which the sample mean is 69, and the standard deviation &#963; = 5. Use &#945;= 0.05.

In a Roper Organization poll of 2000 adults, 1400 have money in regular savings
Accounts. Use this sample data to test the claim that less than( 65- 0.02n)% of all adults have money in regular savings account. Use &#945;= 0.01

Test the claim that&#956;_1=&#956;_2. In the case, the two samples are independent and are randomly selected from populations with normal distributions. Use the data:

Production Method A Production Method B
n1 = 20 n2 = 25
x &#773;1 = 125 +n x &#773;2 = 110 +n
s1 = 15 s2 = 13. Use &#945; = 0.05
5. Suppose that we have selected two independent random samples from two populations having proportions p1 and p2 and that (p_1 ) &#770; = 800/1000 = 0.8 and (p_2 ) &#770; = 950/1000 = 0.95, test the claim that the population proportions are not equal.. Use &#945;= 0.05 .

6. Test the hypothesis given in Problem 10.29 part b. Use &#945;= 0.05+0.001n.

P 10.29 part b
Suppose a sample of 11 paired differences that has been randomly selected from a normally distributed population of paired differences yields a sample mean of d=103.5 and a sample standard deviation of sd = 5.

Part B
Test the null hypothesis Ho:(mu)d> 100 by setting up &#945;(alpha) equal to .05and .01.
How much evidence is there that µd =µ1-µ2 exceeds 100