Question

Assume the population distribution is normally distributed, the weights (in 1000 grams) of a random sample of 10 boxes of cereal are:

10.2 10.1 10.1 9.7 10.3 9.8 9.9 9.8 10.4 10.3

(c) Assume the population standard deviation is given. If one decreases the sample size while keeping the same confidence level, what is the effect on the length of a confidence interval of a population mean? Justify your answer.

(d) Assume the population standard deviation is given. If one increases the confidence level while keeping the same sample size, what is the effect on the length of a confidence interval of a population mean? Justify your answer.

Answer 1

Answer:

Given that:

Assume the population distribution is normally distributed the weights of a random sample of 10 boxes of cereal are

10.2

10.1

10.1

9.7

10.3

9.8

9.9

9.8

10.4

10.3

c)

length of confidence interval

we have

length =

Now is fixed, n decreses,that means increses,hence length of interval increases

d)

Now , n is constant and m increase confidence level i.e we increase ,hence decrese to say this increses the value of to

Length is increases

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