Question

Question 7 1 pts The National High School Health Survey (NHSHS) indicates that about 50% of 12th graders consume less than 300g of vegetables at lunch, about 40% consume 300- 600g, and only 10% of them consume more than 600g. A high school conducted a survey of student diets and health information, and reported data about 12th graders' vegetable intake at lunch: Total Vegetable Intake in gram <300g 300g - 600g > 600g Frequency 150 2 78 98 526 Based on the data, the high school wants to find out whether they have the same proportions of 12th graders in the vegetable intake categories as reported by NHSHS. Step 2. What is the appropriate test statistic? None statistical testing necessary: 150 is different from 278, which is different from 98. ANOVA, because there are 3 groups. O One-sample test of proportion, because the outcome variable is a categorical variable. xgoodness-of-fit test

Answer 1

Solution: The data given in the question statement can be tabulated as below: Vegetable Observed Frequency Expected Frequency f.-felf.- f.) intake <300g 150 526 x 0.50 = 263 -113 12769 300g - 278 526 x 0.40 = 210.4 67.6 4569.76 600g >600g 98 526 x 0.10 = 52.6 45.4 2061.16 Ef. = 526 (f.-f.)/f. 48.551 21.719 39.186 Co-fe)?|fe = 109.456 Chi-square goodness-of-fit test will be used: x2 = {Co Ff*)* = 109.456 Degrees of Freedom = df = (3-1) = 2 P-value: From the x2 distribution table; area under the curve to the right of 109.456 and for (df = 2), is given by: 0.0000 Hence, P-value = 0.0000 Let, significance level = a = 0.05 Since the p-value <a, we reject the null hypothesis. Hence, there is sufficient evidence to conclude that the high school does not have the same proportions of 12th graders in the vegetable intake categories as reported by NHSHS

#hence here we use x2 goodness-of-fit test   is the appropriate test statistic

#option D is correct