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 1720yearold in Canada is μ=298 caloriesAverage \ 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 .H0:μ298.Sample size n=35(large sample,n>30)\Rightarrow H_0:\mu\le298.\\ Sample \ size \ n= 35 (large \ sample, \because n\gt 30)

Sample mean xˉ\bar x = 280

Sample standard deviation (s)=18

Let the null hypothesis be H0:μ298Alternative hypothesisbe H1:μ>298The test statistic is z=xˉμ(sn)z=(280298)(1835)=(18)(1835)=35=5.9161The test statistic z=5.9161For,α=0.01, the critical value is z0.01=2.43Since, the statistic z=5.9161<2.43there is no reason to reject the null hypothesisatα=0.01, using right tail test.We conclude that consumption for students at John Abbottis less than the national average consumption.Let \ the \ null\ hypothesis \ be \ H_0:\mu\le298\\ Alternative \ hypothesis be \ H_1:\mu>298\\ The \ test \ statistic \ is \ z= \frac{\bar x-\mu}{(\frac{s}{\sqrt{n}})} \\ \Rightarrow z=\frac{(280-298)}{(\frac{18}{\sqrt{35}})} \\ =\frac{(-18)}{(\frac{18}{\sqrt{35}})}\\ =-\sqrt{35}\\ =-5.9161 \Rightarrow The \ test \ statistic \ z= -5.9161\\ For, \alpha =0.01, \ the \ critical \ value \ is \ z_{0.01}=2.43\\ Since, \ the \ statistic \ z=-5.9161\lt 2.43\\ there \ is \ no \ reason \ to \ reject \ the \ null \ hypothesis \\ at \alpha=0.01, \ using \ right \ tail \ test.\\ \therefore We \ conclude\ that \ consumption \ for\ students \ at \ John \ Abbott\\ is \ less\ than \ the \ national \ average \ consumption.


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