STATS Misc. Problems Homework

Problem 1)A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFOis less than 1 in every one thousand. State the null hypothesis and the alternative hypothesis fora test of significance.Problem 2)At one school, the average amount of time that tenth-graders spend watching television eachweek is 18.4 hours. The principal introduces a campaign to encourage the students to watch lesstelevision. One year later, the principal wants to perform a hypothesis test to determine whetherthe average amount of time spent watching television per week has decreased. Formulate thenull and alternative hypotheses for the study described.Problem 3)A two-tailed test is conducted at the 5% significance level. What is the P-value required to rejectthe null hypothesis?Problem 4)A two-tailed test is conducted at the 5% significance level. What is the right tail percentilerequired to reject the null hypothesis?Problem 5)What is the difference between an Type I and a Type II error? Provide an example of both.Problem 1)Steven collected data from 20 college students on their emotional responses to classical music.Students listened to two 30-second segments from The Collection from the Best of ClassicalMusic. After listening to a segment, the students rated it on a scale from 1 to 10, with 1indicating that it made them very sad to 10 indicating that it made them very happy. Stevecomputes the total scores from each student and created a variable called hapsad. Steve thenconducts a one-sample t-test on the data, knowing that there is an established mean for thepublication of others that have taken this test of 6. The following is the scores:5.010.013.07.05.014.08.010.03.04.05.03.013.05.015.018.012.07.015.03.0a) Conduct a one-sample t-test. What is the t-test score? What is the mean? Was the testsignificant? If it was significant at what P-value level was it significant?b) What is your null and alternative hypothesis? Given the results did you reject or fail toreject the null and why?(Use instructions on page 349 of your textbook, under Hypothesis Tests with the tDistribution to conduct SPSS or Excel analysis).Problem 2)Billie wishes to test the hypothesis that overweight individuals tend to eat faster than normalweight individuals. To test this hypothesis, she has two assistants sit in a McDonalds restaurantand identify individuals who order the Big Mac special for lunch. The Big Mackers as theybecome known are then classified by the assistants as overweight, normal weight, or neitheroverweight nor normal weight. The assistants identify 10 overweight and 10 normal weight BigMackers. The assistants record the amount of time it takes them to eat the Big Mac special.1.01.01.01.01.01.01.01.01.01.02.02.0585.0540.0660.0571.0584.0653.0574.0569.0619.0535.0697.0782.02.02.02.02.02.02.02.02.0587.0675.0635.0672.0606.0789.0806.0600.0a) Compute an independent-samples t-test on these data. Report the t-value and the pvalues. Were the results significant? (Do the same thing you did for the t-test above,only this time when you go to compare means, click on independent samples t-test.When you enter group variable into grouping variable area, it will ask you to define thevariables. Click define groups and place the number 1 into 1 and the number 2 into 2).b) What is the difference between the mean of the two groups? What is the difference in thestandard deviation?c) What is the null and alternative hypothesis? Do the data results lead you to reject or failto reject the null hypothesis?d) What do the results tell you?Problem 3)Lilly collects data on a sample of 40 high school students to evaluate whether the proportion offemale high school students who take advanced math courses in high school varies dependingupon whether they have been raised primarily by their father or by both their mother and theirfather. Two variables are found below in the data file: math (0 = no advanced math and 1 = someadvanced math) and Parent (1= primarily father and 2 = father and mother).Parent1.01.01.01.01.01.01.01.01.01.01.01.01.01.01.01.01.01.0Math0.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.01.01.02.02.02.02.02.02.02.02.02.02.02.02.02.02.02.02.02.02.02.02.00.00.00.01.01.01.01.01.01.01.01.01.00.00.00.00.00.00.00.00.00.00.0a) Conduct a crosstabs analysis to examine the proportion of female high school studentswho take advanced math courses is different for different levels of the parent variable.b) What percent female students took advanced math classc) What percent of female students did not take advanced math class when females wereraised by just their father?d) What are the Chi-square results? What are the expected and the observed results thatwere found? Are they results of the Chi-Square significant? What do the results mean?e) What were your null and alternative hypotheses? Did the results lead you to reject or failto reject the null and why?Problem Four)This problem will introduce the learner into a technique called Analysis of Variance. For thiscourse we will only conduct a simple One-Way ANOVA and touch briefly on the importantelements of this technique. The One-Way ANOVA is an extension of the independent t test thatcan only look at two independent sample means. We can use the One-Way ANOVA to look atthree or more independent sample means. Use the following data to conduct a One-WayANOVA:Scores1232Group11123445622333Notice the group (grouping) variable, which is the independent variable or factor is made up ofthree different groups. The scores are the dependent variable.Use the instructions for conduction an ANOVA on page 366 of the text for SPSS or Excel.a) What is the F-score; Are the results significant, and if so, at what level (P-value)?b) If the results are significant to the following: Click analyze, then click Compare Means,and then select one-way ANOVA like you did previously. Now click Post Hoc. In thisarea check Tukey. If there is a significant result, we really do not know where it is. Is itbetween group 1 and 2, 1 and 3, or 2 and 3? Post hoc tests let us isolate where the levelof significance was. So if the results come back significant, conduct the post hoc test as Imentioned above and explain where the results were significant.c) What do the results obtained from the test mean?