STATS 250 Lecture Notes - Lecture 11: Mean Absolute Difference, Test Statistic, Statistic

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amberduck8

26 May 2016

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Stats 250: introduction to statistics - lecture 11: testing about a population mean of. Paired difference & learning about the difference in population means. Testing hypotheses about the population mean of paired differences d: A single mean of a population occurs when two quantitative variables are collected in pairs, and we desire information about the difference between the two variables. For paired data designs, it is the differences that we are interested in analyzing. H0: 0 = 0 vs. ha: d > 0. H0: 0 = 0 vs. ha: d < 0. H0: 0 = 0 vs. ha: d 0. Note: the format of the alternative hypothesis depends on the research question of interest and the order in which the differences were taken. Test statistic and conditions for the test. Test statistic = (sample statistic - null value)/standard error = (d-bar - 0)/(sd/ n) If h0 is true, the test statistic has a t(n-1) distribution.

Related Questions

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,:µ = 1420 against Hạ: µ > 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.

beigeserval271

A data set contains information from a random sample of 120 different female dogs who have bred,
40 of which are labradors, 40 are golden retrievers, and 40 are German shepherds.
The variables are:
• Breed: breed of the dog
• LitterSize: the number of pups in the dog’s most recent litter
The data are contained in the file dogs.sav.

(a) [6 marks] Is there evidence of a difference in the population mean litter sizes for the three
breeds? Be sure to state the null and alternative hypotheses, test statistic, null distribution,
p-value, decision, and an appropriate conclusion in plain language.

(b) [3 marks] If appropriate, perform post-hoc tests to determine which breeds have significantly
different mean litter sizes. If post-hoc tests are not appropriate, explain the purpose of a post-hoc
test and why it’s not appropriate in this example.

(c) [2 marks] Report the 95% pairwise confidence interval for the mean difference in litter sizes
between golden retrievers and German shepherds. Interpret this interval with a sentence in plain
language.

(d) [3 marks] What are the assumptions of the analysis performed in part (a)? State whether
each assumption is reasonable with reference to appropriate SPSS output.