Question

how do i solve all six steps?

As quality control manager at a raisin manufacturing and packaging plant, you want to ensure that all the boxes of raisins you sell are comparable, with 30 raisins ( 30) in each box. In the plant, raisins are poured into boxes until the box reaches its sale weight. To determine whether a similar number of raisins are poured into each box, you randomly sample 36 boxes about to leave the plant and count the number of raisins in each. You find the mean number of raisins in each box to be 29.86, with s = 3.87. Perform the six steps of hypothesis testing to determine whether the average number of raisins per box differs from the expected 30.

Answer 1

1)Null hypothesis H₀ : $\mu = 30$

2) Alternative Hypothesis H₁ : $\mu \neq 30$

3) level of significance $\alpha$ = 0.05

4) decision rule

If test statistic is greater than critical value t_{$\alpha$/2,n-1} we reject null hypothesis otherwise fail to reject H₀.

5) test statiostic

given n=36

mean M = 29.86

std dev s = 3.87

t = $\frac{M - \mu}{s/\sqrt{n}} = \frac{29.86 - 30}{3.87/\sqrt{36}}$ = -0.217

degrees of freedom = n-1 = 36 - 1 = 35

critical value = t_0.025,35 = 2.030

6) Since |t| < t_0.025,35 we fail to reject null hypothesis and there is no significant evidence to conclude that the average number of raisins per box is different from expected 30.