Johnny and Billy are two third grade boys. Johnny scored 38 on a stan- dardized reading test with mean 40 and standard deviation 7.5. Billy scored 243 on a standardized reading test with mean 250 and standard deviation 35. Assuming that the given means and standard devia- tions are for equivalent populations of third grade children, (a) which boy reads better, (b) are both boys below average, and (c) are both boys horribly behind in reading or are they both well within the normal range? Answer in full sentences, using z-scores to justify your answer.
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- In a certain test in Calculus, the mean score of a group of 100 students was 30 and the standard deviation was 8. In a test in Physics, the mean was 52 and the standard deviation was 6. If a student scored 65 in Calculus and 70 in Physics, in which test did the student perform better? O The students performed better in their Physics test O The performance is unable to determine. O The students performed the same in both tests. O The students performed better in their Calculus testA sample of 76 female workers and another sample of 48 male workers from a state produced mean weekly earnings of $743.50 for the females and $777.63 for the males. Suppose that the population standard deviations of the weekly earnings are $80.05 for the females and $88.68 for the males. The null hypothesis is that the mean weekly earnings are the same for females and males, while the alternative hypothesis is that the mean weekly earnings for females is less than the mean weekly earnings for males. Directions: • Label your answers with the correct statistical symbols. • If you use the Ti, identify which function and values you used to calculate. If you solve by hand, show all steps 2.5 The significance level for the test is 1%. What is/are the critical value(s)? 2.6. What is the value of the test statistic, rounded to three decimal places? 2.7. What is the p-value for this test, rounded to four decimal places? 2. 8. Using the p-value approach, do you reject or fail to reject the null…. A university examines the variability in the math scores of students accepted to the business and engineering schools. The table below presents sample data from the most recent incoming class.Engineering BusinessSample Standard Deviation 122.4 106.5Sample Size 16 19Perform a hypothesis test to determine whether the variation in math scores is different if ? = 0.05.
- Airline companies are interested in the consistency of the number of babies on each flight, so that they have adequate safety equipment. They are also interested in the variation of the number of Babies. Suppose that an airline executive believes the standard deviation in the number of babies is 6 at the most. The airline conducts a survey. The results of the 23 flights surveyed give a samle mean of 8 with a sample standard deviation of 9. Test the executive's belief to see if it is accurate, or if it is actually greater at the a = 0.05 level. Ho:o = H:o Select an answer df = P-value = The p-value is... greater than a less than (or equal to) a This test statistic leads to a decision to... reject the null fail to reject the null accept the alternative accept the null As such, the final conclusion is that there Select an answer v sufficient evidence to conclude the standard deviation of the number of babies on airplanes is Select an answer than (?Researchers want to compare the relative effectiveness of two popular diets. They randomly assign each of 400 volunteers to one of two Groups: A & B. There are 200 volunteers in each group. Group A spends 6 months on Diet A. Group B spends 6 months on Diet B. At the beginning of the study, the difference in average weight between the two groups was negligible. After the study, the Group A had lost on average 7.8 pounds with a standard deviation of 13.4 pounds, while the Group B had lost on average 5.3 pounds with a standard deviation of 14.8 pounds. Determine the z-score/test statistic for a two-tailed test with significance level α = 0.05 , accurate to 2 decimal places.A personnel psychologist has to decide which of three employees to place in a particular job that requires a high level of coordination. All three employees have taken tests of coordination, but each took a different test. Employee A scored 15 on a test with a mean of 10 and a standard deviation of 2; Employee B scored 350 on a test with a mean of 300 and a standard deviation of 40; and Employee C scored 108 on a test with a mean of 100 and a standard deviation of 16. (On all three tests, higher scores mean greater coordination.) Which employee has the best coordination? (hint: convert raw scores to z scores and compare) Select one: a. Employee A b. Employee B c. Employee C Clear my choice
- Gn. don't provide handwriting solutionA study is conducted to compare the performance of students with more than one personal electronic gadget and those with only one. A number of them were taken as subjects for the study. The mean grades of these students and the standard deviations are shown below: For one gadget: The mean is 83, standard deviation is 12, and sample size is 7. For more than one gadget: The mean is 79, standard deviation is 13, and sample size is 5. Is it possible to conclude that there is no significant difference in the mean grades of the two types of students at a 95% confidence interval? Note: This is a two-tailed test. Also take note that this is finding the difference between two population means.MC Qu. 10-64 Sales at a fast-food restaurant average... Sales at a fast-food restaurant average $6,000 per day. The restaurant decided to introduce an advertising campaign to Increase daily sales. In order to determine the effectiveness of the advertising campaign, a sample of 49 day's sales were taken. The sample showed average daily sales of $6,300. From past history, the restaurant knew that its population standard deviation is about $1,000. If the level of significance is 0.01, have sales increased as a result of the advertising campaign? Multiple Choice Fail to reject the null hypothesis. Reject the null hypothesis and conclude the mean is higher than $6,000 per day. Reject the null hypothesis and conclude the mean is lower than $6,000 per day. Reject the null hypothesis and conclude that mean equal to $6,000 per day.
- ... ... ... ..2) A psychology teacher decided to fail 12% of her class of 40 students. The exam results of the class were roughly normally distributed with a mean of 74 and a standard deviation of 7. A. What score must a student get in order to pass? B. How many students would get a score between 77 and 85?Last year, the average amount that teams for the Statistics Games raised was $375. Have teams been more successful at fundraising this year? To find out, you take a random sample of 36 teams. Your sample of 36 teams yields a mean of $396 and a standard deviation of $70. Might you have made a Type 1 or Type 2 error? A Type 1. This means that we said that the mean amount raised had increased, when it was actually still $375. B You might have made a calculation error. C Neither- we're sure the average has increased. D Type 2. This would mean that we said there was not enough evidence to say the mean had increased from $375, when it actually is higher than $375. E Either kind is possible!