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8. (15 points, 3 each part) Given the summary statistics for independent simple random samples from two populations: ,= 11, s, = 3,n, = 15,= 9,52 = 5, n2 = 14. Use the pooled t-test to perform a two-tailed test for the means for the given significance level a = 0.05. %3D (a) Null hypothesis: Alternative hypothesis: (b) The pooled sample standard deviation Sp = (c) The test statistic t = (d) The critical values are (e) Reject the null hypothesis or not

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Related textbook solutions

Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

Related questions

The queue manager at a bank believes that their clients spend, on average, less than 15 minutes in the queue. To test his belief the manager commissioned a study, which found out that, from a random sample of 80 customers, the average waiting time was 18 minutes. Assume a population standard deviation of 3 minutes and that the waiting time is approximately normally distributed.
(a) Formulate the null and the alternative hypothesis for this test situation. 
(b) Which test statistic (z or t) is appropriate for this test? Give a reason for your answer. 
(c) Conduct a hypothesis test for a single mean at 5% significance level. Interpret your results

A survey in 2010 showed that college students study for a statistics exam on average for three hours and ten minutes. To determine if the average time is changed for the statistics exam data gathered from 81 students in a Midwest University. The sample showed that the average studying time for a statistics exam is two hours and fifty minutes with a standard deviation of one hour and thirty minutes. Let .

a. State the null and alternative hypothesis to be tested.

b. Identify the level of significance.

c. Identify the test statistics.

d. Determine the critical value for this test and formulate a decision rule using the critical value.

e. Compute the test statistics.

f. What do you conclude? Interpret the results.

Use the following scenario for questions 6 – 8. In 2016-17, the average SAT score of the UVA first year class was 1420 out of 1600. An advisor in the statistics department is interested in determining whether statistics majors from that class have higher SAT scores than the average. He tests H,:Β΅ = 1420 against HαΊ‘: Β΅ > 1420, where u is the mean SAT score for statistics majors from the 2016-17 first year class. In a simple random sample of 30 statistics majors, he finds a sample mean SAT score of 1440 with sample standard deviation of 40.

6. What is the value of the test statistic for this significance test?

a. 0.09

b. 0.5

c. 2.73

d. 20

7. From what distribution is this test statistic?

a. N(0, 1)

b. N(1420, 7.30)

c. t distribution with 29 degrees of freedom

d. t distribution with 28 degrees of freedom

8.) The p-value for this test is 0.005. Which of the following is a proper interpretation of this p- value?

a.There is a 0.5% chance that the null hypothesis is true.

b. If the population mean SAT score really is 1420, there's a 0.5% chance that the sample a. mean SAT score from 30 statistics majors would equal 1440.

c.If the population mean SAT score really is 1420, there's a 0.5% chance that the sample mean SAT score from 30 statistics majors would be 1440 or lower.

d. If the population mean SAT score really is 1420, there's a 0.5% chance that the sample mean SAT score from 30 statistics majors would be 1440 or higher.

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