Statistics classwork

You wish to test the following claim (HaHa) at a significance level of α=0.05α=0.05.       Ho:μ=54.4Ho:μ=54.4        Ha:μ<54.4Ha:μ<54.4 You believe the population is normally distributed and you know the standard deviation is σ=18.5σ=18.5. You obtain a sample mean of M=49.2M=49.2 for a sample of size n=41n=41. What is the test statistic for this sample? (Report answer accurate to three decimal places.)  test statistic =  What is the p-value for this sample? (Report answer accurate to four decimal places.)  p-value =  The p-value is...

· less than (or equal to) αα

· greater than αα

This test statistic leads to a decision to...

· reject the null

· accept the null

· fail to reject the null

As such, the final conclusion is that...

· There is sufficient evidence to warrant rejection of the claim that the population mean is less than 54.4.

· There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 54.4.

· The sample data support the claim that the population mean is less than 54.4.

· There is not sufficient sample evidence to support the claim that the population mean is less than 54.4.

Test the claim that the mean GPA of night students is significantly different than 2.3 at the 0.01 significance level. The null and alternative hypothesis would be:

H0:p≥0.575H0:p≥0.575 H1:p<0.575H1:p<0.575

H0:p≤0.575H0:p≤0.575 H1:p>0.575H1:p>0.575

H0:μ≥2.3H0:μ≥2.3 H1:μ<2.3H1:μ<2.3

H0:μ≤2.3H0:μ≤2.3 H1:μ>2.3H1:μ>2.3

H0:p=0.575H0:p=0.575 H1:p≠0.575H1:p≠0.575

H0:μ=2.3H0:μ=2.3 H1:μ≠2.3H1:μ≠2.3

The test is:

right-tailed

two-tailed

left-tailed

Based on a sample of 65 people, the sample mean GPA was 2.32 with a standard deviation of 0.08 The p-value is:  (to 2 decimals) Based on this we:

· Reject the null hypothesis

· Fail to reject the null hypothesis

A poll done for Newsweek found that 17% of Americans have seen or sensed the presence of an angel. A contingent doubts that the percent is really that high. It conducts its own survey. Out of 76 Americans surveyed, only two had seen or sensed the presence of an angel.

· Is the contingent testing a mean or a proportion?

mean

proportion

· The alternate hypothesis, in symbols, is p'p′==>>≥≥<<≤≤0.17.

· Suppose the contingent rejects the claim based on their survey. What type of error could they be making?

Type I

Type II

Test the claim that the proportion of people who own cats is significantly different than 40% at the 0.2 significance level. The null and alternative hypothesis would be:

H0:p≤0.4H0:p≤0.4 H1:p>0.4H1:p>0.4

H0:p≥0.4H0:p≥0.4 H1:p<0.4H1:p<0.4

H0:μ≤0.4H0:μ≤0.4 H1:μ>0.4H1:μ>0.4

H0:μ=0.4H0:μ=0.4 H1:μ≠0.4H1:μ≠0.4

H0:μ≥0.4H0:μ≥0.4 H1:μ<0.4H1:μ<0.4

H0:p=0.4H0:p=0.4 H1:p≠0.4H1:p≠0.4

The test is:

right-tailed

two-tailed

left-tailed

Based on a sample of 700 people, 47% owned cats The p-value is:  (to 2 decimals) Based on this we:

· Fail to reject the null hypothesis

· Reject the null hypothesis

The state of CT claims that the average time on death row is 15 years. A random survey of 75 death row inmates revealed that the average length of time on death row is 17.8 years with a standard deviation of 6.2 years. Conduct a hypothesis to test the state of CT's claim. What type of test should be run?

· z-test of a proportion

· t-test of a mean

The alternative hypothesis indicates a

· left-tailed test

· two-tailed test

· right-tailed test

Calculate the p-value.  What is the decision?

· We reject the claim that the average time on death row is 15 years

· We fail to reject the claim that the average time on death row is 15 years

Proctor & Gamble claims that at least half the bars of Ivory soap they produce are 99.44% pure (or more pure) as advertised. Unilever, one of Proctor & Gamble's competitors, wishes to put this claim to the test. They sample the purity of 139 bars of Ivory soap. They find that 60 of them meet the 99.44% purity advertised. What type of test should be run?

· z-test of a proportion

· t-test of a mean

The alternative hypothesis indicates a

· left-tailed test

· two-tailed test

· right-tailed test

Calculate the p-value.  Does Unilever have sufficient evidence to reject Proctor & Gamble's claim?

· Yes

· No