Reference no: EM132337993

Inferences on 2 Means - Paired Samples Assignment -

Q1. A reading teacher claims that a reading course will increase students' reading speeds. The table below shows reading speeds for 8 students before and after the reading course.

Student	1	2	3	4	5	6	7	8
Before	250	500	450	310	640	200	350	400
After	375	550	425	400	650	280	375	390
Difference d = Before - After

At α = 0.05, is there enough evidence to conclude that the course increases reading speed?

If the course actually increases reading speed, then the reading speed is greater after than before, and the difference, d = Before - After will be negative. The hypotheses are

H₀: μ_d = 0

H₁: μ_d < 0

(a) Complete the table above by calculating the differences in reading speeds.

(b) Construct a normal quantile plot (Sec 6.5) and a box plot for the paired differences. Make rough sketches of the two plots. Is it reasonable to use the paired T-test?

(c) Use STAT/CALC 1: 1-Var Stat to find the mean and standard deviation of the differences:

d-	sd

(d) You will test the hypotheses using a T-Test on the differences. First, give the value of the test statistic.

(e) Then give the P-value.

(f) State your decision (reject the null hypothesis or fail to reject the null hypothesis).

(g) State your conclusion.

(h) Use the TInterval procedure on your calculator to construct a 95% confidence interval for the mean difference in reading speeds. Then interpret the CI using the template on the notes page (remember the 2^nd sentence!)

Q2. To test the belief that sons are taller than their fathers, a student randomly selects 13 fathers who have adult male children. She records the height of both the father and son in inches and gets the following data.

	1	2	3	4	5	6	7	8	9	10	11	12	13
Ht of Father, Xi	70.3	67.1	70.9	66.8	72.8	70.4	71.8	70.1	69.9	70.8	70.2	70.4	72.4
Ht of Son, Yi	74.1	69.2	66.9	69.2	68.9	70.2	70.4	69.3	75.8	72.3	69.2	68.6	73.9

Are sons taller than their fathers?

(a) Complete the list of paired differences d = X_i - Y_i in the table below.

1	2	3	4	5	6	7	8	9	10	11	12	13
-3.8	-2.1

(b) State the null and alternative hypotheses in terms of the mean difference, μ_d. (Remember that, if the son is taller than the father, d will be negative.)

(c) Use the T-test on the paired differences. Give the value of the test statistic.

(d) Give the P-value.

(e) State your decision at the α = 0.05 level.

(f) State your conclusion.

(g) Use the TInterval procedure on your calculator to find a 90% confidence interval for the mean difference in height.

(h) Interpret this confidence interval.

Q3. Interpret calculator display: The following TI-84 Plus calculator display presents the results of a hypothesis test for the mean difference between matched pairs.

a. Is this a left-tailed test, a right-tailed test, or a two-tailed test?

b. How many degrees of freedom are there?

c. What is the P-value?

d. What is the decision at the 0.05 level? Explain.

Q4. Interpret calculator display: The following TI-84 Plus calculator display presents a 99% confidence interval for the mean difference between matched pairs.

a. What is the point estimate of μ_d?

b. How many degrees of freedom are there?

c. Fill in the blanks: We are 99% confident that the mean difference is between _____________ and _________________.