In random samples of 250 persons with low incomes,200 persons with average incomes, and 150 persons withhigh incomes, there were, respectively, 155, 118, and 87who favor a certain piece of legislation. Use the 0.05level of significance to test the null hypothesis θ1 =θ2 = θ3 (that the proportion of persons favoring thelegislation is the same for all three income groups) againstthe alternative hypothesis that the three θ’s are notall equal.

The following histograms represent the heights, measured to the nearest cm, of 14 women and 13 men. Women's heights 3- 2- 1 150 155 160 165 170 175 180 185 190 Height (cm) Men's heights 2 1 0+ 150 155 160 165 170 175 180 185 190 Height (cm) Choose the two options from the list below that are true. Select one or more: Each of the intervals with the lowest frequency in the women's heights dataset contains a smaller number of data values than one of the intervals with the lowest frequency in the men's heights dataset. The histograms are divided into six intervals for the women's heights dataset and eight for the men's heights dataset. The histogram of the women's heights dataset has a greater number of intervals containing two values than the histogram of the men's heights dataset. Both histograms are right-skewed. O The range of the women's heights dataset is greater than the range of the men's heights dataset. Aouan ba Aouan ba

Question 9 Suppose that X is normally distributed with a mean of 40 and a standard deviation of 15. What is P(X> 52.45)? a) O 0.203 b) O 0.597 c) O 0.206 d) O 0.297 e) O 0.207 f). O None of the above

2. 25 values of two variables X and Y are given below. Form a two-way frequency table. Take classes of X as 10 to 20, 20 to 30 etc, that of Y as 100 to 200,200 to 300 etc. X 12 34 33 22 44 37 26 36 55 48 27 52 41 37 21 51 Y 140 266 360 470 470 380 480 315 420 390 440 312 330 390 590 250 X 27 42 43 52 57 44 48 48 69 Y 550 360 570 290 416 380 492 370 590 Obtain (i) the marginal frequency distributions of X and Y. (ii)the conditional distribution of X when Y lies between 300-400. (iii) the conditional distribution of Y when Y lies between 40-50.

Q.6

A researcher selects a random sample of 58 mice from her laboratory. For each mouse, she records the weight of the mouse in grams and whether the mouse prefers Brand A or Brand B food. She would like to know if there is convincing evidence that mouse weight is associated with food preference. Let = 0.10. The observed and expected counts are displayed in the tables. Observed counts: Expected counts: Which of the following contributed the most to the value of the χ2 statistic? average weight and Brand A average weight and Brand B not average weight and Brand A not average weight and Brand B

Which of the following is NOT an assumption of the χ2 test? A. It is appropriate only for ordinal data B. It is a nonparametric test C. The frequency in each cell should be at least 5. D. The sample should be randomly selected.

You are conducting a Goodness of Fit hypothesis test for the claim that the 4 categories occur with the following frequencies:  H0 : pA=0.3;  pB=0.2;  pC=0.2;  pD=0.3  Give all answers as decimals rounded to 3 places after the decimal point, if necessary. Complete the table: Category ObservedFrequency ExpectedFrequency A 30 Correct B 25 Correct C 20 Correct D 34 Correct What is the chi-square test-statistic for this data? Test Statistic: χ2= Correct For a significance of level alpha = 0.01, what is the chi-square critical value? Critical Value: χ2= Incorrect What would be the decision of this hypothesis test? Fail to reject H0   Reject H0   Correct   Remember to round all answers to 3 places after the decimal point, if necessary.