Answer to Question #186039 in Quantitative Methods for Olivia Padula

Question

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?

Answer 1

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

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

Sample mean $\bar x$ = 280

Sample standard deviation (s)=18

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