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 of**25.8** 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 of**25.8** 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)**

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