18. The UMUC MiniMart sells five different types of teddy bears. The manager reports that the five types are equally popular. Suppose that a sample of 1000 purchases yields observed counts 230, 170, 210, 180, and 210 for types 1, 2, 3, 4, and 5, respectively. Use a 0.05 significance level to test the claim that the five types are equally popular. Show all work and justify your answer
( a) Identify the null hypothesis and the alternative hypothesis.
( b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.
( c) Determine the P-value. Show all work; writing the correct P-value, without supporting work, will receive no credit.
( d) Is there sufficient evidence to support the manager’ s claim that the five types of teddy bears are equally popular? Justify your answer
19. A STAT 200 instructor believes that the average quiz score is a good predictor of final exam score. A random sample of 10 students produced the following data where x is the average quiz score and y is the final exam score. x 80 93 50 60 100 40 85 70 75 85 y 72 95 75 68 90 35 83 60 77 85
( a) Find an equation of the least squares regression line. Show all work; writing the correct equation, without supporting work, will receive no credit.
( b) Based on the equation from part( a), what is the predicted final exam score if the average quiz score is 90? Show all work and justify your answer
20. A study of 10 different weight loss programs involved 500 subjects. Each of the 10 programs had 50 subjects in it. The subjects were followed for 12 months. Weight change for