SCI1020 Statistical Reasoning Please type in the answers Question 4 (10 marks) M

Question

SCI1020 Statistical Reasoning
Please type in the answers
Question 4 (10 marks) Many cheeses are produced in the shape of a wheel. Because of slight variations in the consistency of a cheese, the average weight varies from wheel to wheel. The production output is supposed to have an average weight of at least 500g per wheel and samples are taken to check this. One random sample of 16 wheels of Brie cheese had a mean weight of 515.5 grams with a standard deviation of 66.5 grams. The populations of the cheeses are known to have a normal distribution of weights. Detemine if the sample shows that the production output above does not have the correct average weight per wheel by calculating the 90% confidence interval for the mean weight of cheese wheel

Explanation / Answer

sol:

90% Confidedence inetrval for the true population mean is given by

=sample mean-margin of error and sample mean+margin of error

margin of error=t crit * sample sd(sqrt(n)

ALpha=0.1(for 90%)

df=n-1=16-1=15

alpha/2=0.1/2=0.05

t crit for 0.05 level of signiificance and 15 df =1.753

margin of error=1.753(66.5)/sqrt(16)

=29.14363

90% CI is

515.5-29.1463,515.5+29.1463

=486.4,544.6

lower limit=486.4

upper limit=544.6

486.4<mu<544.6

Thes limits does not contain the hypothesis value of true mean=500

Reject Null hypothesis

Accept Alternative Hypothesis

Null hypothesis was :mu<500

Alternative Hypothesis:mu>=500

Alpha=0.10

Alternative Hypothesis was claim

Conclusion:

there is sufficient evidence at 5% level of significance to conclude that the the avergae weight of atleast 500g

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