Kroeger claimed that it created a new type of artificial meat that has an averag

Question

Kroeger claimed that it created a new type of artificial meat that has an average lifetime of at least 1650 days. The lifetime is approximately normally distributed with variance of 245. A consumer group designed a test to decide if there is evidence to refute the company's claim. They chose a significance level of alpha = 0.05 and randomly selected 32 pieces of meat| to evaluate. a) Describe the null hypothesis and the alternative hypothesis. b) If the true mean found by the consumer group is mu = 1644, what is the power of this test? c) What can the consumer group do to increase the power of the test? d) What sample size should the consumer group utilize to achieve a power of 0.9 while maintaining the same significance level of alpha = 0.05 if the true mean is 1644 rather than 1650?

Explanation / Answer

a)null hypothesis: mean >=1650

alternate hypothesis: mean <1650

b)here std deviation =(245)1/2 =15.65

hence std error =std deviation/(nj)1/2 =2.767

for 0.05 level; zcritical =1.64485

hence critical value =mean +z*std error =1650-1.64485*2.767=1645.4487

hence power of test =P(X<1645.4487)=P(Z<(1645.4487-1644)/2.767)=P(Z<0.5235)=0.6997

c)consumer group can increase sample size to increase power

d)for power 0.9 ; value of critical point =1644+1.28155*15.65/(n)1/2 =1650-1.64485*15.65/(n)1/2

45.80/(n)1/2=6

n~59

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