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##### Statistics P5T5 Assignment Problems

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Question;Question 1;A medical doctor claims that the proportion of female;patients with high blood-pressure is smaller than the proportion of male;patients with high blood-pressure. The doctor conducted a survey in his;practise. Out of the 100 female patients only 13 had high;bloodpressure and out of the 110 male patients, 33 had high bloodpressure.;1.1 Test the doctors? claim at a 5% level of significance.;Assume that the population proportions are equal.;1.2 Construct a 90% confidence interval for the difference;between the two population proportions.;1.3 Compute the p-value;Question 2;An experimenter is concerned that variability of responses;using two different experimental procedures may not be the same. He randomly;selects two samples of 16 and 14 responses from two normal populations and gets;the statistics: S 12 = 55 and S22 = 118 respectively. Do the sample variances;provide enough evidence at the 10% significance level to infer that the two;population variances;differ?;Question 1;1. TABLE 10-10;The following EXCEL output contains the results of a test to;determine if the proportions of satisfied guests at two restaurants are the;same or different.;Hypthesized Difference;Level of Significance;GROUP 1;Number of Successes;Sample Size;GROUP 2;Number of Successes;Sample Size;Group 1 Proportion;Group 2 Proportion;Difference in Two Proportions;Average Proportion;Test Statistic;TWO-TAIL TEST;Lower Critical Value;Upper Critical Value;p-Value;0;0.05;163;227;154;262;0.718061674;0.58778626;0.130275414;0.648261759;3.00875353;-1.959961082;1.959961082;0.002623357;Referring to Table 10-10, allowing for 0.75% probability of;committing a Type I error, what are the decision and conclusion on testing;whether there is any difference in the proportions of satisfied guests in the;two restaurants?;Do not reject the null hypothesis, there is enough evidence;to conclude that there is significant difference in the proportions of;satisfied guests at the two restaurants.;Do not reject the null hypothesis, there is not enough;evidence to conclude that there is significant difference in the proportions of;satisfied guests at the two restaurants. Reject the null hypothesis, there is;enough evidence to conclude that there is significant difference in the;proportions of satisfied guests at the two restaurants.;Reject the null hypothesis, there is not enough evidence to;conclude that there is significant difference in the proportions of satisfied;guests at the two restaurants.;Question 2;1. TABLE;10-12;The dean of a college is interested in the proportion of;graduates from his college who have a jobOFFER on graduation day. He is;particularly interested in seeing if there is a difference in this;proportion for accounting and economics majors. In a random;sample of 100 of each type of major at graduation, he found that 65 accounting;majors and 52 economics majors had job OFFERS. If;the accounting majors are designated as "Group 1";and the economics majors are designated as "Group 2," perform the;appropriate hypothesis test using a level of significance of 0.05.;Referring to Table 10-12, the hypotheses the dean should use;are;H0:? 1 -? 2 = 0 versus H1:?;1;-?2?0;H0:? 1 -? 2? 0 versus H1:? 1 -? 2 = 0;H0:? 1 -? 2?0 versus H1:? 1 -? 2 > 0;H0:? 1 -? 2?0 versus H1:? 1 -? 2 0;H0:? 1 -? 2?0 versus H1:? 1 -? 2 0;H0:? 1 -? 2?0 versus H1:? 1 -? 2 0;H0:? 1 -? 2?0 versus H1:? 1 -? 2 < 0;Question 5;2.;TABLE 10-10;The following EXCEL output contains the results of a test to;determine if the proportions of satisfied guests at two;restaurants;are the same or different.;Hypthesized Difference;Level of Significance;GROUP 1;Number of Successes;Sample Size;GROUP 2;Number of Successes;Sample Size;Group 1 Proportion;Group 2 Proportion;Difference in Two Proportions;Average Proportion;Test Statistic;TWO-TAIL TEST;0;0.05;163;227;154;262;0.718061674;0.58778626;0.130275414;0.648261759;3.00875353;Lower Critical Value;Upper Critical Value;p-Value;-1.959961082;1.959961082;0.002623357;Referring to Table 10-10, if you want to test the claim that;Restaurant;1 (Group 1) has a higher proportion of satisfied customers;compared;to Restaurant 2 (Group 2)", the p-value of the test;will be;0.00262;0.00262/2;2*(0.00262);1-(0.00262/2);Question 6;1.;TABLE 10-11;A corporation randomly selects 150 salespeople and finds;that;66% who have never taken a self-improvement course would;like;such a course. The firm did a similar study 10 years ago in;which;60% of a random sample of 160 salespeople wanted a;selfimprovement course. The groups are assumed to be independent;random samples. Let? 1 and? 2 represent the true;proportion of;workers who would like to attend a self-improvement course;in the;recent study and the past study, respectively.;Referring to Table 10-11, what is the estimated standard;error of;the difference between the two sample proportions?;0.629;0.500;0.055;0;Question 7;1.;TABLE 10-11;A corporation randomly selects 150 salespeople and finds;that;66% who have never taken a self-improvement course would;like;such a course. The firm did a similar study 10 years ago in;which;60% of a random sample of 160 salespeople wanted a;selfimprovement course. The groups are assumed to be independent;random samples. Let? 1 and? 2 represent the true;proportion of;workers who would like to attend a self-improvement course;in the;recent study and the past study, respectively.;Referring to Table 10-11, what is the value of the test;statistic to;use in evaluating the alternative hypothesis that there is a;difference in the two population proportions?;4.335;1.96;1.093;0;Question 8;1.;In testing for differences between the means of two related;populations, the null hypothesis is;H0:?D = 2.;H0:?D = 0.;H0:?D 0.;Question 9;3.;TABLE 10-10;The following EXCEL output contains the results of a test to;determine if the proportions of satisfied guests at two;restaurants;are the same or different.;Hypthesized Difference;Level of Significance;GROUP 1;Number of Successes;Sample Size;GROUP 2;Number of Successes;Sample Size;Group 1 Proportion;Group 2 Proportion;Difference in Two Proportions;Average Proportion;Test Statistic;TWO-TAIL TEST;Lower Critical Value;Upper Critical Value;p-Value;0;0.05;163;227;154;262;0.718061674;0.58778626;0.130275414;0.648261759;3.00875353;-1.959961082;1.959961082;0.002623357;Referring to Table 10-10, if you want to test the claim that;Restaurant;1 (Group 1) has a lower proportion of satisfied customers;compared;to Restaurant 2 (Group 2)", you will use;a t-test for the difference between two proportions.;a z-test for the difference between two proportions.;an F test for the difference between two proportions.;a x2 test for the difference between two proportions.;Question 10;1.;TABLE 10-11;A corporation randomly selects 150 salespeople and finds;that;66% who have never taken a self-improvement course would;like;such a course. The firm did a similar study 10 years ago in;which;60% of a random sample of 160 salespeople wanted a;selfimprovement course. The groups are assumed to be independent;random samples. Let? 1 and? 2 represent the true;proportion;of workers who would like to attend a self-improvement;course in;the recent study and the past study, respectively.;Referring to Table 10-11, what is/are the critical value(s);when;testing whether population proportions are different if? =;0.10?;? 1.645;? 1.96;-1.96;? 2.08

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