Exam 22: Paired Samples and Blocks

A test of abstract reasoning is given to a random sample of students before and after they completed a formal logic course.The results are given below.Construct a 95% confidence interval for the mean difference between the before and after scores if $\overline { \mathrm { d } }$ (before - after)= 3.7 and sd = 4.945 start text Before end text 74 83 75 88 84 63 93 84 91 77 After 73 77 70 77 74 67 95 83 84 75

A study was conducted to determine the average number of words children learn during their third year.For a random sample of one hundred children,parents reported the number of words spoken at 24 months and then again at 36 months of age.A 98% confidence interval for the difference of the means at 36 months and 24 months,μ36 - μ24,was determined to be $( 200,277 ) .$

An agricultural company wanted to know if a new insecticide would increase corn yields.Eight test plots showed an average increase of 3.125 bushels per acre.The standard deviation of the increases was 2.911 bushels per acre.Determine a 90% confidence interval for the mean increase in yield.

A researcher was interested in comparing the salaries of female and male employees of a particular company.Independent random samples of 8 female employees (sample 1)and 8 male employees (sample 2)yielded the following weekly salaries (in dollars). Female Male 495 722 760 562 556 880 904 520 540 600 1005 1250 743 750 660 1640

A researcher wishes to determine whether listening to music affects students' performance on memory test.He randomly selects 50 students and has each student perform a memory test once while listening to music and once without listening to music.He obtains the mean and standard deviation of the 50 "with music" scores and obtains the mean and standard deviation of the 50 "without music scores".

Ten different families are tested for the number of litres of water they use per week before and after viewing a conservation video.Construct a 90% confidence interval for the mean of the difference of the "before" minus the "after" times if $\overline { \mathrm { d } }$ (before - after)= 4.8 and sd = 5.2451 Before 33 33 38 33 35 35 40 40 40 31 After 34 28 25 28 35 33 31 28 35 33

Ten different families are tested for the number of litres of water they use each week before and after viewing a conservation video.We want to see if there is strong evidence that the conservation video changes people's water consumption rate.A t-test of the null hypothesis of no difference has a t-statistic of -2.894 with a P-value of 0.0178.Interpret this result by explaining the meaning of the P-value.

Five students took a math test before and after tutoring.Their scores were as follows. Subject A B C D E Before 71 75 69 75 78 After 75 84 67 78 90 Do the data suggest that the tutoring improves math scores on average? Perform a paired $\text { t-test }$ at the 10% significance level.

The ages of 100 married male/female couples was recorded for a particular population.It was observed that out of the 100 couples,53 men were older the woman,32 women were older than the man,and 15 couples were the same age.Is the median difference in age between married men and women different from 0? Carry out a Sign Test.Assume the couples are a representative sample from the population.Use a significance level of 0.05.

A researcher was interested in examining the difference in the number of hours of sleep married women and single women get each night.Five married women and five single women reported their average number of hours of sleep per night for the last week.Shown below is software output for two possible tests for the data. Paired t-test of μ(1-2) Test Ho: μ(S - M)= 0 vs HA: μ(S - M)≠ 0 Mean of Paired Differences = 1.6 t-Statistic = 4 w/4 df p = 0.0161 2-Sample t-Test of μ1 - μ2 Ho: μS - μM = 0 Ha: μS - μM ≠ 0 Test H0: μ(S)- μ(M)= 0 vs HA: μ(S)- μ(M)≠ 0 Difference Between Means = 1.6 t-Statistic = 1.8353 w/7.27 df p = 0.1075 Which of these tests is appropriate for these data? Explain.Using the test you select,state your conclusion.

Ten different families were tested for the average number of litres of water they used per week before and after viewing a conservation video.A 95% confidence interval for the difference of the means after and before the training,μA - μB,was determined to be (-10.3,-4.1).

Ten different families are tested for the number of litres of water they use each week before and after viewing a conservation video.We want to see if there is strong evidence that the conservation video reduces people's water consumption rate.A t-test of the null hypothesis of no difference has a t-statistic of -2.894 with a P-value of 0.0089.State your conclusion regarding the hypotheses.If this conclusion is incorrect,which type of error was made?

A coach uses a new technique to train gymnasts.7 gymnasts were randomly selected and their competition scores were recorded before and after the training.The results are shown below. Subject A B C D E F G Before 9.5 9.4 9.7 9.6 9.6 9.4 9.4 After 9.6 9.6 9.7 9.5 9.7 9.7 9.2 Do the data suggest that,on average,the training technique is effective in raising the gymnasts' scores? Perform a paired t-test at the 5% significance level.

Ten different families are tested for the number of litres of water a week they use before and after viewing a conservation video.Do the data suggest that the mean amount after the viewing differs from the mean amount before the viewing? Perform a paired $\text { t-test }$ at the 5% significance level. Before 33 33 38 33 35 35 40 40 40 31 After 34 28 25 28 35 33 31 28 35 33

An agricultural company wants to know if a new insecticide would increase corn yields.They will use test plots to collect observations with and without the insecticide.If they want to estimate the mean increase with a margin of error of 1.2 bushels per acre,with 95% confidence,estimate the minimum number of test plots they need.A previous study showed that the standard deviation of the increases was about 2.9 bushels per acre.

A researcher is interested in investigating whether people perform better at dexterity tests while listening to classical music or to no music.He designs a dexterity test,and first gives it to his participants while classical music is playing,and then while no music is playing.

A test of abstract reasoning is given to a random sample of students before and after they completed a formal logic course.The results are given below.Do the data suggest that the mean score after the course differs from the mean score before the course? Perform a paired $\text { t-test }$ at the 5% significance level. Before 74 83 75 88 84 63 93 84 91 77 After 73 77 70 77 74 67 95 83 84 75

The table below shows the weights of seven subjects before and after following a particular diet for two months. Subject A B C D E F G Before 156 196 152 182 172 167 200 After 149 187 150 187 158 169 188 Do the data suggest that,on average,the diet is effective in reducing weight? Perform a paired $\text { t-test }$ at the 1% significance level.

The violent crime rate (number of violent crimes per 100,000 residents)is investigated for nine Canadian cities for the years 1990 and 2000 to see if there has been a change. City A B C D E F G H I Violent crime rate in 2000 Violent crime rate in 1990 325 250 199 785 645 259 855 679 301 in 379 355 175 925 750 405 1005 902 455 Is there evidence that the violent crime rate has decreased? Suppose you had mistakenly treated these data as two independent samples instead of matched pairs.What would the significance test have found? Explain why the results are so different.

The violent crime rate (number of violent crimes per 100,000 residents)is investigated for ten Canadian cities for the years 1990 and 2000 to see if there has been a change.Shown below is software output for two possible tests. Paired t-test of μ(1-2) Test H0: μ (2000 - 1990)= 0 vs HA: μ(2000 - 1990)≠ 0 Mean of Paired Differences = 110.7 t-Statistic = -2.632 w/9 df p = 0.0273 Two-sample t-test of μ1 - μ2 H0: μ1 - μ2 = 0 HA: μ1 - μ2 ≠ 0 Test H0: μ(2000)- μ(1990)= 0 vs HA: μ(2000)- μ(1990)≠ 0 Difference Between Means = 110.7 t-Statistic = -0.9222 w/15.6 df p = 0.3705 Which of these tests is appropriate for these data? Explain.Using the test you select,state your conclusion.