Is my Answer to: Is the Price in NY is 20% higher than that in LA, right?

in Statistics / Test for the mean. Independent Samples (Part 2)

H0: μNY -μLA >= 0.20 (20%)
while
H1: μNY - μLA < 0.20 (20%)
Formula:
T score= (Percentage mean difference - hypothesized mean difference )/ standard error

Percentage mean difference = (Sample mean NY - Sample Mean LA) / Sample Mean LA
= (3.94 - 3.25) / 3.25 = 0.69 / 3.25 = 0.212

T score = ((0.69 / 3.25) - 0.20) / 0.11
T score = 0.112

t_statistic for 10 + 8 -2 = 16 degrees of freedom at 0.05 significance, one-sided test = 1.746

T score < t statistic hence accept the null hypothesis

p-value = 0.4561 > 0.05 hence accept the null hypothesis
p-value = 0.4561 > 0.01 hence accept the null hypothesis at 0.01 significance level

Therefore the price of apples in NY is statistically proven to be higher than 20% the price of apples in LA at all common and many uncommon significance levels

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