1) A supermarket chain wants to determine any difference between the proportion of morning shoppers who are men and the proportion of evening shoppers who are men. A random sample of 400 morning shoppers showed that 130 were men. A random sample of 480 evening shoppers showed 187 to be men. Use a 5% level of significance to test for a significant difference in the proportion of morning and evening male shoppers. What is your conclusion?
2. Shipments of light bulbs are acceptable to a distributor if the mean life is at least 1000 hours. A random sample of 48 light bulbs is take and a test is to be done at the 1% level of significance. Assume that the population standard deviation is 50 hours. What is the probability of making a Type II error if the “true” mean is 985 hours?
please answer in this form if possible…(example)
Ho: mu1=mu2
Ha: mu1 not equal to mu2
t=(xbar1-xbar2)/sqrt(s1^2/n1+s2^2/n2)=(116900-115700)/sqrt(2300^2/21+1750^2/26)=1.97
Given a=0.05, the critical value is t(0.025, df=n1+n2-2=45)=2.01
Since t=1.97 is less than 2.01, we do not reject HO. So we can not conclude that there is a difference in the asking price in the two cities.
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