Part 1: To assess the accuracy of a laboratory scale, a standard weight known to

Question

Part 1: To assess the accuracy of a laboratory scale, a standard weight known to weigh 10 grams is weighed repeatedly. The scale readings are normally distributed with unknown mean (this mean is 10 grams if the scale has no bias). The standard deviation of the scale readings is known to be 0.0005 gram.

(a) The weight is measured five times. The mean result is 10.0023 grams. Give a 98% confidence interval for the mean of repeated measurements of the weight. (Round your answers to four decimal places.)

(?,?) (up yo four decimal places)

Part 2:Some of the methods in this section are approximations rather than exact probability results. We have given rules of thumb for safe use of these approximations.

(a) You are interested in attitudes toward drinking among the 75 members of a fraternity. You choose 30 members at random to interview. One question is "Have you had five or more drinks at one time during the last week?" Suppose that in fact 30% of the 75 members would say "Yes." Explain why you cannot safely use the B(30, 0.3) distribution for the count X in your sample who say "Yes."

The population (the 75 members of the fraternity) is only 2.5 times the size of the sample. Our rule of thumb says that this ratio should be at least (ANSWER HERE) .

(b) The National AIDS Behavioral Surveys found that 0.2% (that's 0.002 as a decimal fraction) of adult heterosexuals had both received a blood transfusion and had a sexual partner from a group at high risk of AIDS. Suppose that this national proportion holds for your region. Explain why you cannot safely use the Normal approximation for the sample proportion who fall in this group when you interview an SRS of 1000 adults.

Our rule of thumb for the Normal approximation calls for np and n(1 p) to be at least (ANSWER HERE) ; we have np = (1000)(0.002) = 2.

Please Answer all parts

Explanation / Answer

Ans:

1)population standard deviation is known,so use z distribution.

z value for 98% Confidence interval is 2.33

98% Confidence interval

=10.0023+/-2.33*(0.0005/sqrt(5))

=10.0023+/-2.33*0.000224

=10.0023+/-0.000521

=(10.0018,10.0028)

2)a)Rule of thumb :

10% condition states that sample sizes should be no more than 10% of the population.

here sample size is 30,which is 40% of the population.

b)n=1000

p=0.002

np=1000*0.002=2

As,np<10,so Normal approximation is not valid.

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