Question

William, a chef, claims that his meatball weight is not equal to 3 ounces, on average. Several of his customers do not believe him, so he decides to do a hypothesis test, at a 1% significance level, to persuade them. He cooks 19 meatballs. The mean weight of the sample meatballs is 2.9 ounces. William knows from experience that the standard deviation for his meatball weight is 0.5 ounces. H0: μ=3; Ha: μ≠3 α=0.01 (significance level) What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places? Provide your answer below:

Answer 1

Answer: -0.87

Step-by-step explanation:

As per given , we have

$\mu=3$

$\overline{x}=2.9\\\\ \sigma=0.5$

Sample size : n= 19

Test statistic : $z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

By substituting the corresponding values , we get

$z=\dfrac{2.9-3}{\dfrac{0.5}{\sqrt{19}}}\\\\=-0.871779788708\approx0.87$  [Rounded to the nearest two decimal places.]

Hence, the test statistic (z-score) of this one-mean hypothesis test= -0.87