Experiments on learning in animals sometimes measure how long it takes mice to find their way through a maze. The mean time is 18 seconds for one particular maze. A researcher thinks that a loud noise will cause the mice to complete the maze faster. She measures how long each of the 10 mice takes with a noise as stimulus. The sample mean is 16.5 seconds.
Part 3:Hypothesis Testing Question 1. Experiments on learning in animals sometimes measure how long it takes mice to find their way through a maze. The mean time is 18 seconds for one particular maze. A researcher thinks that a loud noise will cause the mice to complete the maze faster. She measures how long each of the 10 mice takes with a noise as stimulus. The sample mean is 16.5 seconds. a) Construct the null and the appropriate hypothesis for the researcher, perform the statistical test for the researcher. b) The assistant researcher decided to test the null hypothesis against the alternative What would be the conclusion of his test? Question 2. Let a random sample of n=100 be taken from a normal population with unknown mean and standard deviation equal to 9. What critical value of sample mean should be used to test the null hypothesis that the mean is 20 against alternative the mean is greater than 20, for a 2% level of significance? Suppose the sample size is doubled to 200, what is the new critical value of the sample mean? Question 3. Random samples each of size n are drawn from each population. State the distribution of Obtain symmetric 95% confidence intervals for and for . The following test of hypothesis that is proposed. The hypothesis will be rejected only if the 95% confidence intervals for and have no point in common. What conclusion is reached when and the values of and are 10 and 11 respectively? How will you modify your answer if the variance from each population was unknown, give the assumptions for your approach. Question 4. A factory has two production lines A and B for the manufacture of a certain article. A random sample of 250 articles from line A is found to contain 14 defectives while a random sample of 350 articles from line B is found to contain 28 defectives. Is there evidence of a real difference between the proportions of defective articles produced by the two lines? Question 5. You plan to conduct a survey to find what proportion of the workforce has two or more jobs. You decide on a 90% confidence level and state that the estimated proportion must be within the 2% of the population proportion. A pilot survey reveals that 5 of 50 sampled hold two or more jobs. How many in the workers should be interviewed to meet your requirements? Repeat the exercise assuming a 95% confidence level and comment. Question 6. In two wards for elderly women in a geriatric hospital the following levels of haemoglobin were found: Ward A: 12.2, 11.1, 14.0, 11.3, 10.8, 12.5, 12.2, 11.9, 13.6, 12.7, 13.4, 13.7 g/dl; Ward B: 11.9, 10.7, 12.3, 13.9, 11.1, 11.2, 13.3, 11.4, 12.0, 11.1 g/dl. What is the difference between the mean levels in the two wards? What is the 95% confidence interval for the difference in treatments? Question 7. Each of five varieties of corn is planted in three plots in a large field. The respective yields, in bushels per acre, are listed below. Variety 12345 46.249.260.348.952.5 51.958.658.751.454.0 48.757.460.444.649.3 Test whether the differences among the average yields are statistically significant. Show the ANOVA table. Let 0,05 be the level of significance. Part 4:Goodness of Fit Question 1. The table below shows delinquency-by-birth- order, for a selected sample of 1154 girls in a high school. The cross classification of the data is given below: .Birth Order OldestIn betweenYoungest Only Child DelinquentYes24293523 No45031221170 Percent Yes5.18.514.224.7 Perform a statistical test to test whether or not the birth order is related to juvenile delinquency at 5% level of significance. Which birth order contributed most to your test statistic? Discuss Question 2 Suppose that we wanted to test normality of the Etruscan-skull data. Data collected on 84 Etruscan-skull is classified as follows: Skull Width (mm) Observed Frequency 125-1291 130-1344 135-13910 140-14433 145-14924 150-1549 155-1593 Test at 5% level of significance, whether these data follow the normal distribution. Question 3 Table below gives the number of years in which x wars broke out. Carry out a goodness of fit for the Poisson model with parameter ( at 10% level of significance) i) and ii) unknown parameter Number of wars, x. Beginning in a given year 0 1 2 3 4+ Observed frequency 223 142 48 15 15