Question

Construct a confidence interval for ?d, the mean of the differences d for the population of paired data. Assume that the population of paired differences is normally distributecd 21) A coach uses a new technique in training middle distance runners. The times for 9 differen 21) athletes to run 800 meters before and after this training are shown below Athlete A BC D EF G H I Time before training (seconds) 115.2 120.9 108.0 112.4 107.5 119.1 121.3 110.8 122.3 116.0 119.1 105.1 111.9 109.1 115.2 118.5 110.7 120.9 Time after training Construct a 99% confidence interval for the mean difference of the "before-minus-after" times A) -0.82 < Hd < 3.26 C) -0.85 Hd <3.29 B) -0.54 <Hd <2.98 D)-0.76 Hd <3.20 Assume that a hypothesis test of the given claim will be conducted. Identify the typeI or type I error for the test 22) A medical researcher claims that 10% of children suffer from a certain disorder. Identify the 22) type I error for the test. A) Reject the claim that the percentage of children who suffer from the disorder is different B) Fail to reject the claim that the percentage of children who suffer from the disorder is C) Fail to reject the claim that the percentage of children who suffer from the disorder is D) Reject the claim that the percentage of children who suffer from the disorder is equal to from 1096 when that percentage really is different from 1096. equal to 10% when that percentage is actually 10%. equal to 10% when that percentage is actually different from 10%. 10% when that percentage is actually 10% 23) The principal of a school claims that the percentage of students at his school that come from 23) single-parent homes is 11%. Identify the type ll error for the test A) Fail to reject the claim that the percentage of students that come from single-parent B) Reject the claim that the percentage of students that come from single-parent homes is C) Fail to reject the claim that the percentage of students that come from single-parent D) Reject the claim that the percentage of students that come from single-parent homes is homes is equal to 11% when that percentage is actually 11%. equal to 11% when that percentage is actually less than 11%. homes is equal to 11% when that percentage is actually different from 11%. equal to 11% when that percentage is actually 11%.

Answer 1

21) Computing the Confidence Intervals for ?_d

_{2 Use t-table with d仁n-1 When samples are matched or paired, difference scores are computed for each participant or between members of a matched pair, and "n" is the number of participants or pairs, x is the mean of the difference scores, and Sd is the standard deviation of the difference scores}

upper limit = (115.2778 - 114.0556 )+ 3.8325 * ( 1.826046/3) = 3.26

lower limit = (115.2778 - 114.0556 ) - 3.8325 * ( 1.826046/3) = -0.82

Correct option- A) -0.82 < mu <3.26

22) Null hypothesis : The percentage of children who suffer from the disorder is different from 10 %

Alternate hypothesis : The percentage of children who suffer from the disorder is 10 %

Type I error is Probability of rejecting null hypothesis when null hypothesis is true.

Correct option- A) Reject the claim that the percentage of children who suffer from the disorder is different from 10 % when that percentage really is different from 10 %

23) Null hypothesis : the percentage of students that come from single-parents homes is not equal to 11%

Alternate hypothesis : The percentage of students that come from single-parents homes is equal to 11%

Type II error is Probability of accepting null hypothesis when alternate hypothesis is true.

Correct option- D) Reject the claim that the percentage of students that come from single-parents homes is equal to 11% when that percentage is actually 11%