Extending the Concepts and Skills
10.60 In this section, we introduced the pooled t-test, which provides a method for comparing two population means. In deriving the pooled t-test, we stated that the variable
cannot be used as a basis for the required test statistic because “is unknown. Why can’t that variable be used as a basis for the required test statistic?
Want to see the full answer?
Check out a sample textbook solutionChapter 10 Solutions
Introductory Statistics (10th Edition)
- n a test of H0: p = 0.4 against H1: p ≠ 0.4, a sample of size 100 produces Z = 1.28 for the value of the test statistic. Thus the p-value (or observed level of significance) of the test is approximately equal toarrow_forwardIs the difference between the mean annual salaries of statisticians in Region 1 and Region 2 more than $8000? To decide, you select a random sample of statisticians from each region. The results of each survey are shown to the right. At α=0.10, what should you conclude?arrow_forwardAttachedarrow_forward
- 276 CHAPTER 9 INTRODUCTION TO THE t STATISTIC 10. To evaluate the effect of a treatment, a sample of n = 8 is obtained from a population with a mean of p %3D 40, and the treatment is administered to the %3D individuals in the sample. After treatment, the sample mean is found to be M = 35. a. If the sample variance is s? = 32, are the data suf- ficient to conclude that the treatment has a signifi- cant effect using a two-tailed test with a = .05? b. If the sample variance is s? cient to conclude that the treatment has a significant effect using a two-tailed test with a = .05? c. Comparing your answer for parts a and b, how does the variability of the scores in the sample influence the outcome of a hypothesis test? %3D 72, are the data suffi-arrow_forwardYou want to determine the effect of soap on bacterial colonies. In order to make sure that the environmentdoes not affect your experiment, you divide 13 different petri dishes in half - one side is exposed to soap, theother is a control.You measure the number of colonies that grow in each petri dish and come up with the following results:petri dish 1 2 3 4 5 6 7 8 9 10 11 12 13soap 10 5 7 10 19 11 13 17 19 8 11 10 16control 20 17 11 17 26 18 21 25 24 17 17 17 21Perform a complete hypothesis test to see if there is a difference in bacterial colonies between the soapand control dishes.Again - notice that you are given no advice. You need to figure this out on your own, althoughthis one should be a bit easier than (4). Feel free to use R to solve this problem, just make sureyou don't just hand in a printout.arrow_forwardI need help with t= and the p-value ? Please help asaparrow_forward
- You receive a brochure from a large university. The brochure indicates that the mean class size for full-time faculty is fewer than 33 students. You want to test this claim. You randomly select 18 classes taught by full-time faculty and determine the class size of each. The results are shown in the table below. At α=0.05, can you support the university's claim? Complete parts (a) through (d) below. Assume the population is normally distributed. 383132313042242527253035323025313024arrow_forwardExplain this by showing tables gow to solve step steparrow_forwardStep 2 (b) Compute o², the variance of x. The variance, 6², of a probability distribution is used to describe the spread of the values of the random variable. The formula for the variance of a probability distribution is given below. 0²= [(x-μ)²f(x) The mean, μ, is needed to calculate the variance. We found E(x) = μ = 8. Again, the use of a table will help organize the necessary values to find the variance. X 4 8 12 x-μ 48-4 Submit 0 Need Help? 4 Thus, the variance is ² 4 Read It (x-μ)² (-4)² = 16 0 = 5 X Skip (you cannot come back) f(x) 0.25 16(0.25) = 0.50 0.25 X (x-µ)²f(x) 0² 0 1 4 5 X = Σ(x-μ)²F(x) Xarrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill