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.
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Student
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1
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2
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3
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4
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5
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6
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7
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8
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Before
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250
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500
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450
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310
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640
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200
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350
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400
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After
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375
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550
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425
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400
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650
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280
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375
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390
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Difference d = Before - After
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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: μd = 0
H1: μd < 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) 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 2nd 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.
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1
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2
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3
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4
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5
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6
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7
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8
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9
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10
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11
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12
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13
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Ht of Father, Xi
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70.3
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67.1
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70.9
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66.8
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72.8
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70.4
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71.8
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70.1
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69.9
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70.8
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70.2
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70.4
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72.4
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Ht of Son, Yi
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74.1
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69.2
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66.9
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69.2
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68.9
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70.2
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70.4
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69.3
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75.8
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72.3
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69.2
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68.6
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73.9
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Are sons taller than their fathers?
(a) Complete the list of paired differences d = Xi - Yi in the table below.
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1
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2
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3
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4
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5
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6
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7
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8
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9
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10
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11
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12
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13
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-3.8
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-2.1
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(b) State the null and alternative hypotheses in terms of the mean difference, μd. (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 μd?
b. How many degrees of freedom are there?
c. Fill in the blanks: We are 99% confident that the mean difference is between _____________ and _________________.