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