Question

A random sample of 64 bags of white cheddar popcorn weighed, on avarage, 5.23 ounces with a standard deviation of 0.24 ounces. Test the hypothesis that mean = 5.5 ounces against the alternative hypothesis, mean < 5.5 ounces at the 0.05 level of significance.

Answer 1

$n=64 \\ \bar{x}=5.23 \\ s= 0.24 \\ H_0: \mu = 5.5 \\ H_1: \mu <5.5$

Test-statistic:

$t = \frac{\bar{x}- \mu}{s / sqrt{n}} \\ t = \frac{5.23-5.5}{0.24 / \sqrt{64}} = -9 \\ α=0.05$

Critical value $t_{n-1, α} = t_{63,0.05}= -1.6694$

Since $|t| > t_{n-1, α}$ we reject H₀ and conclude, that $\mu <5.5$ at 0.05 level of significance.