# STA100C -Homework 9-Scientists have used Mongolian gerbils

1STA100C fall 2016 Homework 9Due at the beginning of class on Monday November 28, 2016Note new due date and change of due dates for remaining homeworkshomeworkdue9Monday 11/28/1610Friday 12/02/16Points lost if youdon’t follow the ruleall points (no credit) Write your section number on the right side at the top of the first page.MAKE SURE YOU WRITE THE SECTION YOU ARE REGISTERED FORWrite your name and student ID1on the left side at the top of the first page.Your name should be spelled exactly the same as it is on SmartSiteall points (no credit)(no nicknames please)Write the homework number in the middle at the top1of the first page. (Any format is fine, for example, HW1, homework 1, etc.)Staple all pages.1If your homework is on paper pulled out of a notebook,cut off all of the fringes (from the torn horizontal threadsthat attached the paper to the notebook).1For example, for homework 9 if your name is John Smith, your student ID is 123456789, andyou are in section C01, then the top of your first page should look like thisJohn Smith123456789 Homework 9 C01 Be kind to the grader.• make sure you write your name clearly (so it is easy to read)• write neatly• circle all final answers (so they are easy to find)Round all test statistics to two digits after the decimal point. Round all p-values to fourdigits after the decimal point. You should do the rounding after the last step in the calculations. If you round in intermediate steps the rounding error tends to accumulate.You should do most of the calculations in this assignment without using R (you will needR to get the p-values). However, if you want to check your chi-square tests with R there issome R code for chi-square tests on SmartSite under Resources ? R resources ? chi squaretest in R.pdf 21. Scientists have used Mongolian gerbils when conducting neurological research. A certain breed of these gerbils was crossed and gave progeny of the following colors.colornumber of progeny black40 brown59 white42 Are these data consistent with the 1:2:1 ratio predicted by a certain genetic model?Use a chi-square test with ? = 0.05.(a) Calculate the expected numbers of black, brown, and white gerbils assuming thatthe null hypothesis that the ratio is 1:2:1 is true.(b) Calculate the chi-square test statistic.(c) If ? = 0.05, what is the critical value? You can either get this from table 9 inyour book (also on SmartSite) or use the following R command.qchisq(1-alpha,degf)where alpha is the alpha level and degf is the degrees of freedom.(d) Use the chi-square table (table 9 in your book and also on SmartSite) to find aninterval contains the p-value. (See page 319 of lecture notes.)(e) Calculate a p-value using the following R command.(1-pchisq(TS,df=degf))where TS is the test statistic and degf is the degrees of freedom.Note that we don’t multiply by 2 because the chi-square test is always testing thenull against a non-directional alternative.(f) At ? = 0.05, do the data provide evidence the genetic model does not hold? Howdid you make your decision?2. Geneticists studying the inheritance pattern of cowpea plants classified the plants inone experiment according to the nature of their leaves. The data are as follows:typenumber I179 II III44 23 Test the null hypothesis that the three types occur with probabilities 12/16, 3/16, and1/16. Use a chi-squared test with ? = 0.1(a) Calculate the expected numbers of types I, II, and III assuming the null hypothesisis true.(b) Calculate the chi-square test statistic.(c) If ? = 0.1, what is the critical value?(d) Use the chi-square table (table 9 in your book and also on SmartSite) to find aninterval contains the p-value. (See page 319 of lecture notes.)(e) Calculate the p-value.(f) At ? = 0.1 do the data provide evidence against the null hypothesis? How didyou make your decision? 33. A survey is conducted in a large high to study the relationship between sex and alcohol.Results are given in the following table.drinkersmales58females46total104 non-drinkers425496 total100100200 Define p1 as the proportion of male and p2 as the proportion of female students in thishigh school who consume alcohol on a regular basis. Use a chi-square test to test thenull hypothesis H0 : p1 = p2 against the alternative hypothesis HA : p1 6= p2 .(a) Find the expected number of males who are drinkers assuming the null hypothesisof no difference between males and females is true.Note that given this one expected number the three other expected numbers canbe found by subtraction from either the row or column totals.(b) Calculate the chi-square test statistic.(c) What are the degrees of freedom for this test?(d) If ? = 0.1, what is the critical value?(e) Use the chi-square table (table 9 in your book and also on SmartSite) to find aninterval contains the p-value. (See page 319 of lecture notes.)(f) Calculate the p-value.(g) At ? = 0.1 do the data provide evidence against the null hypothesis? How didyou make your decision?4. For a study of a population of the fruitfly Drosophila subobscura, researchers placedbaited traps in two woodland sites and one open-ground area. The numbers of maleand female flies trapped in a single day are given below.woodland site 1males89females31total120 woodland site 2342054 open ground total74197136187210384 Use a chi-square test with ? = 0.05 to compare the sex ratios at the three sites. Thenull and alternative hypotheses areH0 : sex and site are independentHA : sex and site are not independent(a) Calculate the chi-square test statistic.(b) What are the degrees of freedom for the test?(c) If ? = 0.05, do the data provide evidence in favor of the alternative hypothesis.How did you make your decision?