Question

1)When a truckload of apples arrives at a packing plant, a random sample of 225 is selected and examined for bruises, discoloration, and other defects. The whole truckload will be rejected if more than 10% of the sample is unsatisfactory. Suppose that in fact 12% of the apples on the truck do not meet the desired standard. What’s the probability that the shipment will be accepted anyway? Give your answer to 4 decimal places.

2-1) In 1960, census results indicated that the age at which American men first married had a mean of 24.5 years. It is widely suspected that young people today are waiting longer to get married. We want to find out if the mean age at first marriage has increased during the past 40 years. We plan to test our hypothesis by selecting a random sample of 50 men who married for the first time last year.The men in our sample married at an average age of25.8 years, with a standard deviation of 4.79 years. What is the p - value for this hypothesis test? Let all the necessary assumptions for inference be satisfied. Give your answer to 4 decimal places.

2-2) In 1960, census results indicated that the age at which American men first married had a mean of 24.5 years. It is widely suspected that young people today are waiting longer to get married. We want to find out if the mean age at first marriage has increased during the past 40 years. We plan to test our hypothesis by selecting a random sample of 50 men who married for the first time last year.The men in our sample married at an average age of25.8 years, with a standard deviation of 4.79 years. What is the test statistic for this hypothesis test? Let all the necessary assumptions for inference be satisfied. Give your answer to 4 decimal places.

Answer 1

1)

population proportion ,p=   0.12          
n=   225          
              
std error , SE = √( p(1-p)/n ) =    0.022          
              
sample proportion , p̂ =   0.1000          
Z=( p̂ - p )/SE=    (0.1-0.12)/0.0217)=       -0.923  
P ( p̂ <    0.100   ) =P(Z<( p̂ - p )/SE) =   -0.923  
              
=P(Z <    -0.923   ) =    0.1780   (answer)