This problem is from Open Intro Statistics 2nd ed. book: http://www.openintro.or

Question

This problem is from Open Intro Statistics 2nd ed. book: http://www.openintro.org/stat/down/oiStat2_05.pdf

• The National Center of Education Statistics conducted a survey of high school seniors, collecting test data on reading, writing, and several other subjects. Here we examine a simple random sample of 200 students from this survey, and their scores on the reading and writing tests.

• The observed differences in scores (for reading score minus writing score) for each student was analyzed. For this sample, the mean was –0.545 and the standard deviation was 8.887 points.

• The question being considered is whether the average reading score and average writing score are basically the same or not. Do these data provide convincing evidence of a difference between the average scores on the two exams?

Note: a Test of Hypothesis is not normally numbered this way! These numbers are simply for the Discussion Forum assignment.

Use the 0.05 significance level in this test.

1. Is this situation about two Independent Samples or about Matched Pairs (dependent samples)? Explain why you decided as you did.

2. State the null and alternative hypotheses in words (as sentences). Label which is which.

3. State the null and alternative hypotheses in symbolic form. Use correct notation. Label which is which.

4. Do the data meet the conditions for using our method of testing the hypothesis? Clearly show why or why not. And make a conclusion: are the conditions met?

5. For this test , is the test statistic a Z distribution or T distribution or something else? Explain how you know. Write the Formula for the test statistic (NOT with numbers, just the general formula).

6. Find the value of the test statistic, as a decimal value rounded to 4 decimal places. Explain how you found it (formula used – with what numbers? Or calculator command – what one exactly?)

7.. Do NOT find the p-value in this step, but prepare to find it by:

a) Determine if this is a left-tail, right-tail, or 2-tail test.

b) Shade the portion of the curve that is relevant to finding the p-value.

c) And label relevant number(s) on the horizontal axis.

8. Find the p-value a) Write the calculator command you use. b) State the p-value, rounded to 4 decimal places.

9. a) Are the results significant?

b) HOW do you know? (why did you decide that?)

c) State any and all of these that are correct conclusions: Reject H0 Do not reject H0 Accept H0 Data do not support Ha Data support Ha

10. Write a sentence or two in clear English stating the conclusion in the context of the problem. So, include words from the statement of the situation. E.g. in this case: reading scores, writing scores

Explanation / Answer

1.This is a case of Matched Pairs ( dependent samples) since each pair of observation is taken on the same individual and reading and writing scores of an individual are in any way interrelated.

2.Null hypothesis -> H0 : population mean of reading score = population mean of writing score
Alternative hypothesis -> H1 : not H0

3. Null hypothesis -> H0 : 1 = 2
Alternative hypothesis -> H1 : 1 2

5. The test statistic is a T-distribution since here the standard deviation of the difference in scores of the population is unknown and we are using the standard deviation obtained from the sample.
Test statistic : T = n * mean(difference in scores) / s.d(difference in scores)

6. T = 200*(-0.545)/8.887 = -0.8673

7. a)This is a two-tailed test.

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