Answer to Question #186039 in Quantitative Methods for Olivia Padula

Question #186039

Consumption of sugar-sweetened beverages has increased over the years. Individuals aged 17-20, were surveyed in 2020 across the 10 provinces to determine the number of calories consumed by sugar-sweetened beverages. The average consumption for 17-20-year-old in Canada is 298 calories. You decide to test if the average calorie consumption for students at John Abbott will be less than the national average. You select a random sample of 35 students and your results show that the average sugar-based calorie consumption is 𝑋" = 280, s=18. Do John Abbott students consume significantly fewer sugar-sweetened calories? Set alpha to 0.01 Find Null and research hypothesis 1 or 2 tailed? Find critical value? find test statistic?


1
Expert's answer
2021-04-28T07:25:54-0400

"Average \\ consumption \\ for\\ 17-20-year-old\\ in\\ Canada\\ is\\ \\mu =298 \\ calories" \\

To test if the average calorie consumption for students at John Abbott will be less than the national average ."\\Rightarrow H_0:\\mu\\le298.\\\\\n\nSample \\ size \\ n= 35 (large \\ sample, \\because n\\gt 30)"

Sample mean "\\bar x" = 280

Sample standard deviation (s)=18

"Let \\ the \\ null\\ hypothesis \\ be \\ H_0:\\mu\\le298\\\\\nAlternative \\ hypothesis be \\ H_1:\\mu>298\\\\\nThe \\ test \\ statistic \\ is \\ z= \\frac{\\bar x-\\mu}{(\\frac{s}{\\sqrt{n}})} \\\\\n\\Rightarrow z=\\frac{(280-298)}{(\\frac{18}{\\sqrt{35}})} \\\\\n=\\frac{(-18)}{(\\frac{18}{\\sqrt{35}})}\\\\\n=-\\sqrt{35}\\\\\n=-5.9161\n\\Rightarrow The \\ test \\ statistic \\ z= -5.9161\\\\\nFor, \\alpha =0.01, \\ the \\ critical \\ value \\ is \\ z_{0.01}=2.43\\\\\nSince, \\ the \\ statistic \\ z=-5.9161\\lt 2.43\\\\\nthere \\ is \\ no \\ reason \\ to \\ reject \\ the \\ null \\ hypothesis \\\\\nat \\alpha=0.01, \\ using \\ right \\ tail \\ test.\\\\\n\\therefore We \\ conclude\\ that \\ consumption \\ for\\ students \\ at \\ John \\ Abbott\\\\\n is \\ less\\ than \\ the \\ national \\ average \\ consumption."


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