A simple random sample of 35 observations is derived from a normally distributed

Question

A simple random sample of 35 observations is derived from a normally distributed population with a known standard deviation of 6.3. Use Table 1.

A simple random sample of 35 observations is derived from a normally distributed population with a known standard deviation of 6.3. Use Table 1.

Is the condition that is normally distributed satisfied? Yes No

b. Compute the margin of error with 95% confidence. (Round intermediate calculations to 4 decimal places, "z" value and final answer to 2 decimal places.)

  Margin of error   

c. Compute the margin of error with 90% confidence. (Round intermediate calculations to 4 decimal places, "z" value and final answer to 2 decimal places.)

  Margin of error   

d. Which of the two margins of error will lead to a wider interval? The margin of error with 90% confidence. The margin of error with 95% confidence.

Explanation / Answer

There is no data given in the question , however is hall show you the formulae and you can use them on any data

Margin of error is given as Z* SE and Standard error is SE = SD/sqrt(N) , where N = sample size and SD = standard deviation

now for 95% Confidence interval we see the z table as 1.96 hence the margin of error becomes

1.96* SD/(sqrt(N))

c) For 90% confidence the only difference would be in terms of the Z multiplier , so for 90% this value is

1.645* SE =

1.645 * SD/Sqrt(N)

d)

please note that when we reduce the confidence interval the scope of error increases , which is caused by an increase in the width of the interval .

so if the confidence interval is increased then this width decreases and vice versa , there is an inverse relationship.

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