Montarello and Martins (2005) found that fifth grade students completed more mathematics problems correctly when simple problems were mixed in with their regular math assignments. To further explore this phenomenon, suppose that a researcher selects a standardized mathematics achievement test that produces a normal distribution of scores with a mean of µ= 100 and a standard deviation of σ = 24. The researcher modifies the test by inserting a set of very easy problems among the standardized questions and gives the modified test to a sample of n = 36 students. If the average test score for the sample is M = 120, is this result sufficient to conclude that inserting the easy questions improves student performance? Use a one-tailed test with α = .05. The null  hypothesis in words is

A graduate student is interested in how viewing different types of scenes affects working memory. For his study, he selects a random sample of 36 adults. The subjects complete a series of working memory tests before and after walking in an urban setting. Before the walk, the mean score on the test of working memory was 9.1. After the walk, the mean score was 1.4 higher. The graduate student has no presupposed assumptions about how viewing different types of scenes affects working memory, so he formulates the null and alternative hypotheses as: H00 : μDD = 0 H11 : μDD ≠ 0 Assume that the data satisfy all of the required assumptions for a repeated-measures t test. The graduate student calculates the following statistics for his hypothesis test: Mean difference (MDD) 1.4 Estimated population standard deviation of the differences (s) 1.6 Estimated standard error of the mean differences (sMDMD) 0.2667 Degrees of freedom (df) 35 The t statistic 5.25 The critical values of t…

Three experiments investigating the relation between need for cognitive closure and persuasion were performed. Part of the study involved administering a "need for closure scale" to a group of students enrolled in an introductory psychology course. The "need for closure scale" has scores ranging from 101 to 201. For the 75 students in the highest quartile of the distribution, the mean score was x = 176.90. Assume a population standard deviation of ? = 7.71. These students were all classified as high on their need for closure. Assume that the 75 students represent a random sample of all students who are classified as high on their need for closure. Find a 95% confidence interval for the population mean score ? on the "need for closure scale" for all students with a high need for closure. (Round your answers to two decimal places.)

An educational psychologist is studying two methods of tutoring young children: Method A and Method B. She wants to test whether there is any difference in puzzle solving skills between children tutored by one method versus children tutored by the other. Independent samples of 10 children who were tutored using Method A and 11 children who were tutored using Method B were chosen at random. The Method A children took a mean of 40 minutes to solve a certain puzzle with a standard deviation of 6 minutes. The Method B children took a mean of 44 minutes to solve the same puzzle with a standard deviation of 7 minutes. Assume that the two populations of completion times are normally distributed and that the population variances are equal. Construct a 90% confidence interval for the difference u, - u, between the mean puzzle-solving times for Method A children ( u) and for Method B children (µ,). Then find the lower limit and upper limit of the 90% confidence interval. Carry your intermediate…

A professor is concerned that the two sections of college algebra that he teaches are not performing at the same level. To test his claim, he looks at the mean exam score for a random sample of students from each of his classes. In Class 1, the mean exam score for 13 students is 75.1 with a standard deviation of 5.8. In Class 2, the mean exam score for 16 students is 82.6 with a standard deviation of 7.3. Test the professor's claim at the 0.02 level of significance. Assume that both populations are approximately normal and that the population variances are equal. Let Class 1 be Population 1 and let Class 2 be Population 2. Step 2 of 3: Compute the value of the test statistic. Round your answer to three decimal places.

Dr. Sylvester Stallone is a circadian rhythms researcher and believes sleep affects memory.  Having collected data on a large number of subjects who are getting the recommended amount of sleep, he knows the mean digit span of this population is 5.6 digits.  To test his hypothesis, he measures the digit span of 15 volunteers randomly selected from the population, after depriving them of one night’s sleep.  The results show a mean (X bar) of 4.1 and a standard deviation of (s) 1.4.        a.   What does Dr. Stallone conclude, using and alpha of 0.05 (two tailed)?         b. If appropriate, calculate the size of effect and provide an interpretation of the value?

A professor is concerned that the two sections of college algebra that he teaches are not performing at the same level. To test his claim, he looks at the mean exam score for a random sample of students from each of his classes. In Class 1, the mean exam score for 12 students is 80.8 with a standard deviation of 5.7. In Class 2, the mean exam score for 14 students is 84.5 with a standard deviation of 4.9. Test the professor's claim at the 0.01 level of significance. Assume that both populations are approximately normal and that the population variances are equal. Let Class 1 be Population 1 and let Class 2 be Population 2. Step 2 of 3: Compute the value of the test statistic. Round your answer to three decimal places.