Answer
$\bar{x}$ =$\frac{∑X}{n}$
=$\frac{1527}{10}$
= 152.7
s^2 = $\frac{ n(∑X^2) - [(∑X)^2] }{n(n-1)}$
= $\frac{2336630- 2331729}{10*9}$
=54.4556
s = $ \sqrt 54.4556 \ $
s =7.3794
a $\bar{x}$ =152.7 calories μ=150 calories,σ=7.3794 calories$σ_\bar{s}$ =$ \frac{7.3794}{$10}$=2.334, n = 10
α = 0.025, df = 10-1=9, critical value=2.262
t=$ \frac{\bar{x}-μ }{σ_\bar{s}}$
= $ \frac{152.7-150 }{2.334}$
=-1.16
Rejection region =z > -2.262
Non rejection region = z <= -2.262
The value z = -1.16 falls within the rejection region, hence we reject the null hypothesis and conclude that 8-ounce low fat-yogurt cups contain on average , more than 150 calories per cup.
Work Step by Step
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