SOLUTION: Mavuso recently graduated with a Diploma in business statistics and got a position in one of the leading retail company as a supervisor. Mavuso works in the bakery department and h

Question 1145197: Mavuso recently graduated with a Diploma in business statistics and got a position in one of the leading retail company as a supervisor. Mavuso works in the bakery department and he has noted that there is a huge variance in the budgeted amount of flour spent and number of loaves produced. Mavuso suspect that this could be as a result of those preparing the dough not doing their job properly. There are chances that the loaves being sold by the company are above the stipulated weight of 700 grams.
In order to back his claim with statistical empirical evidence Mavuso sampled 40 loaves and obtained the following weights 720, 712, 713, 699, 610, 721, 710, 710, 711, 701, 705, 702, 712, 715, 713, 713, 715, 722, 701, 713, 715, 696, 699, 685, 711, 721, 710, 705, 712, 701, 712, 703, 701, 712, 700, 722, 721, 698, 699 and 715.
REQUIRED:
Use hypothesis test analysis to validated or dispute the claim? At 10 % significant level and make a recommendation to the management.

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
sample mean is 706.4 grams and sample standard deviation is 17.76 grams
:
company mandates 700 grams for the mean
:
Ho: x = 700
H1: x not = 700
:
This is a two-tailed hypothesis test
:
alpha(a) = 0.10
:
critical probability(p*) = 1 - (a/2) = 0.95
:
sample size is 40 > 30, we can use the normal distribution
:
standard error(SE) = 17.76/square root(40) = 2.8
:
test statistic is (706.4 - 700)/2.8 = 2.29
:
At the 10% significance level, the critical value for a two-tailed test is found from the table of z-scores to be 1.645 or -1.645
:
Since the test statistic(2.29) does fall within the critical region(2.29 > 1.645), we reject the null hypothesis(Ho)
:
Recommendation to management: Determine source of over-weight - maybe the scales used or need for employee education
:

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