The distribution of professional baseball player salaries has a mean of $3.2 million. An analyst believes that the mean salary for teams on the East Coast is different. The analyst randomly selects 50 baseball players from teams on the East Coast and records their annual salaries. The mean salary for the players in the sample is $3.9 million with a standard deviation of $2.1 million. A significance test at an alpha level a = 0.05 of produces a P-value of 0.02. What is the correct interpretation of the P-value?
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- A report about how American college students manage their finances includes data from a survey of college students. Each person in a representative sample of 793 college students was asked if they had one or more credit cards and if so, whether they paid their balance in full each month. There were 500 who paid in full each month. For this sample of 500 students, the sample mean credit card balance was reported to be $825. The sample standard deviation of the credit card balances for these 500 students was not reported, but for purposes of this exercise, suppose that it was $195. Is there convincing evidence that college students who pay their credit card balance in full each month have a mean balance that is lower than $907, the value reported for all college students with credit cards? Carry out a hypothesis test using a significance level of 0.01. Find the test statistic and P-value.In a test of the effectiveness of garlic for lowering cholesterol, 36 subjects were treated with raw garlic. Cholesterol levels were measured before and after the treatment. The changes (before minus after) in their levels of LDL cholesterol (in mg/dL) have a mean of 0.6 and a standard deviation of 2.43. Use a 0.05 significance level to test the claim that with garlic treatment, the mean change in LDL cholesterol is greater than 0. What do the results suggest about the effectiveness of the garlic treatment? Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim. What are the null and alternative hypotheses? Ο Α. Ho : μ=0 mg/dL B. Ho: µ= 0 mg/dL H1: µ#0 mg/dL H1: µ 0 mg/dL O D. Ho: µ= 0 mg/dL H1: µ >0 mg/dL H1:µ<0 mg/dL Determine the test statistic. (Round to two decimal places as needed.) Determine the P-value. (Round to three decimal places as needed.)…A bank wonders whether omitting the annual credit card fee for customers who charge at least $3000 in a year will increase the amount charged on its credit cards. The bank makes this offer to an SRS of 400 of its credit card customers. It then compares how much these customers charge this year with the amount that they charged last year. The mean increase in the sample is $246, and the standard deviation is $112. Is there significant evidence at the 1% level that the mean amount charged increases under the no-fee offer? State H0 and Ha and carry out a significance test.
- Mean entry-level salaries for college graduates with mechanical engineering degrees and electrical engineering degrees are believed to be approximately the same. A recruiting office thinks that the mean mechanical engineering salary is actually lower than the mean electrical engineering salary. The recruiting office randomly surveys 50 entry-level mechanical engineers and 60 entry-level electrical engineers. Their mean salaries were $46,100 and $46,700, respectively. Their standard deviations were $3,450 and $4,210, respectively. Conduct a hypothesis test to determine if you agree that the mean entry-level mechanical engineering salary is lower than the mean entry-level electrical engineering salary.Solve the following problems. Use the steps in conducting hypothesis tests.Insurance Company A claims that its customers pay less for car insurance, on average, than customers of its competitor, Company B. You wonder if this is true, so you decide to compare the average monthly costs of similar insurance policies from the two companies. For a random sample of 15 people who buy insurance from Company A, the mean cost is $150 per month with a standard deviation of $14. For 6 randomly selected customers of Company B, you find that they pay a mean of $157 per month with a standard deviation of $11. Assume that both populations are approximately normal and that the population variances are equal to test Company A's claim at the 0.05 level of significance. Let customers of Company A be Population 1 and let customers of Company B be Population 2. Step 3 of 3: Draw a conclusion and interpret the decision.Community college instructors' salaries in one state are very low, so low that educators in that state regularly complain about their compensation. The national mean is $51,809 but instructors from Mississippi claim that the mean in their state is significantly lower. They survey a simple random sample of 33 colleges in the state and calculate a mean salary of $45,068 with a standard deviation of $15,261. Test the instructors' claim at the 0.05 level of significance. Step 1 of 3: State the null and alternative hypotheses for the test. Fill in the blank below Step 2 of 3: Compute the value of the test statistic. Round your answer to three decimal places. Step 3 of 3: Draw a conclusion and interpret the decision
- Automobile collision insurance is used to pay for any claims made against the driver in the event of an accident. This type of insurance will typically pay to repair any assets that your vehicle damages. A random sample of 40 collision claims of 20- to 24-year-old drivers results in a mean claim of $4580 with a standard deviation of $2291. An independent random sample of 40 collision claims of 30- to 59-year-old drivers results in a mean claim of $3680 with a standard deviation $2036. Using the concept of hypothesis testing, determine if a higher insurance premium should be paid by 20- to 24-year-old drivers. Use a a = 0.10 level of significance, and let population 1 be 20- to 24-year old drivers and population 2 be 30- to 59-year old drivers. Complete pa through (e) below. (a) Collision claims tend to be skewed right. Why do you think this is the case? O A. There are many large collision claims relative to the majority of claims.A report states that the mean yearly salary offer for students graduating with a degree in accounting is $48,738. Suppose that a random sample of 50 accounting graduates at a large university who received job offers resulted in a mean offer of $49,830 and a standard deviation of $3800. Do the sample data provide strong support for the claim that the mean salary offer for accounting graduates of this university is higher than the national average of $48,738? Test the relevant hypotheses using ? = 0.05. (Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to three decimal places.) t = P-value =Researchers conducted an experiment to test the effects of alcohol. Errors were recorded in a test of visual and motor skills for a treatment group of 28 people who drank ethanol and another group of 28 people given a placebo. The errors for the treatment group have a standard deviation of 2.20, and the errors for the placebo group have a standard deviation of 0.77. Assume that the two populations are normally distributed. Use a 0.05 significance level to test the claim that both groups have the same amount of variation among the errors. Let sample 1 be the sample with the larger sample variance, and let sample 2 be the sample with the smaller sample variance. What are the null and alternative hypotheses? OB. Ho: 0=02 O A. H₁: 0²12 = 0²/2 H₁:0² > 0²/2 H₁:0² <0² O C. Ho: 0²/02/ H₁:0² = 0² Identify the test statistic. (Round to two decimal places as needed.) Use technology to identify the P-value. (Round to three decimal places as needed.) What is the conclusion for this hypothesis test?…
- Community college instructors' salaries in one state are very low, so low that educators in that state regularly complain about their compensation. The national mean is $57,636, but instructors from Mississippi claim that the mean in their state is significantly lower. They survey a simple random sample of 37 colleges in the state and calculate a mean salary of $52,534 with a standard deviation of $15,791. Test the instructors' claim at the 0.05 level of significance. Step 2 of 3: Compute the value of the test statistic. Round your answer to three decimal places. E Tables E Keypad Answer Keyboard ShortcutsA report states that the mean yearly salary offer for students graduating with mathematics and statistics degrees is $62,915. Suppose that a random sample of 50 mathematics and statistics graduates at a large university who received job offers resulted in a mean offer of $63,200 and a standard deviation of $3,700. Do the sample data provide strong support for the claim that the mean salary offer for mathematics and statistics graduates of this university is greater than the national average of $62,915? Test the relevant hypotheses using a = 0.05. USE SALT Find the test statistic and P-value. (Use technology to calculate the P-value. Round your test statistic to two decimal places and your P-value to four decimal places.) t = P-value = State your conclusion. O Reject Ho. We have convincing evidence that the mean salary offer for mathematics and statistics graduates of this university is greater than the national average of $62,915. Fail to reject H. We have convincing evidence that the…In a test of the effectiveness of garlic for lowering cholesterol, 36 subjects were treated with raw garlic. Cholesterol levels were measured before and after the treatment. The changes (before minus after) in their levels of LDL cholesterol (in mg/dL) have a mean of 0.7 and a standard deviation of 23.1. Use a 0.01 significance level to test the claim that with garlic treatment, the mean change in LDL cholesterol is greater than 0. What do the results suggest about the effectiveness of the garlic treatment? Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.