Question

1) The state of CT claims that the average time in prison is 15 years. A random survey of 75 inmates revealed that the average length of time in prison is 16.4 years with a standard deviation of 6.7 years. Conduct a hypothesis to test the state of CT's claim.

What type of test should be run?

• t-test of a mean
• z-test of a proportion

The alternative hypothesis indicates a

• right-tailed test
• left-tailed test
• two-tailed test

Calculate the p-value. Keep all decimal places of accuracy.

What is the decision?

• We fail to reject the claim that the average time in prison is 15 years
• We reject the claim that the average time in prison is 15 years

2) Links claims that at least half the bars of Ivory soap they produce are 99.44% pure (or more pure) as advertised. Unilever, one of Links competitors, wishes to put this claim to the test. They sample the purity of 102 bars of Ivory soap. They find that 41 of them meet the 99.44% purity advertised.

What type of test should be run?

• t-test of a mean
• z-test of a proportion

The alternative hypothesis indicates a

• two-tailed test
• right-tailed test
• left-tailed test

Calculate the p-value.

Does Unilever have sufficient evidence to reject Links claim?

• Yes
• No

3) Given ˆpp^ = 0.2286 and N = 35 for the high income group,

Test the claim that the proportion of children in the high income group that drew the nickel too large is smaller than 50%. Test at the 0.1 significance level.

a) Identify the correct alternative hypothesis:

• μ=.50μ=.50
• μ>.50μ>.50
• p<.50p<.50
• μ<.50μ<.50
• p=.50p=.50
• p>.50p>.50

Give all answers correct to 3 decimal places.

b) The test statistic value is:   

c) Using the P-value method, the P-value is:

d) Based on this, we

• Reject H0H0
• Fail to reject H0H0

e) Which means

• There is not sufficient evidence to support the claim
• The sample data supports the claim
• There is not sufficient evidence to warrant rejection of the claim
• There is sufficient evidence to warrant rejection of the claim

4) You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ=20.5σ=20.5. You would like to be 90% confident that your estimate is within 10 of the true population mean. How large of a sample size is required?

n =

Use a critical value accurate to three decimal places, and do not round mid-calculation

Answer 1

1)

The provided sample mean is X = 16.4 and the sample standard deviation is s = 6.7, and the sample size is n = 75. (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: u = 15 Ha: u 7 15 This corresponds to a two-tailed test for which a t-test for one mean, with unknown population standard deviation will be used. (2) Rejection Region Based on the information provided, the significance level is a = 0.05, and the critical value for a two-tailed test is te = 1.993. The rejection region for this two-tailed test is R= {t: \t| > 1.993} (3) Test Statistics The t-statistic is computed as follows: X - μo t= 16.4 – 15 6.7/75 1.81 s/n (4) Decision about the null hypothesis Since it is observed that t| = 1.81 <tc = 1.993, it is then concluded that the null hypothesis is not rejected. Using the P-value approach: The p-value is p = 0.0744, and since p= 0.0744 > 0.05, it is concluded that the null hypothesis is not rejected. (5) Conclusion It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean u is different than 15, at the 0.05 significance level. Confidence Interval The 95% confidence interval is 14.858 <u < 17.942. Graphically T-Test Results: t-stats = 1.81, p-value =0.0744 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

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