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# Value sample and interval

I am having problems with these sample problems. Can you please help me? I have attached the following questions within an excel sheet for your usage in deriving the solutions.

A 90 % confidence interval for a situation is developed and is given by the following 48 < µ < 64.
a) Give the value of the sample mean that was used in developing this interval.
b) Give the value of the margin of error that was used in developing this interval.

Calculate the appropriate critical z-value for each of the following confidence levels?
a) 95% confidence interval
b) 80% confidence interval

What happens to the size (width) of a confidence interval in a problem if:
a) the percent of desired confidence (confidence level) increases from 80% to 90%? Does it get wider or narrower?
b) the size of the sample used to produce the confidence interval is decreased?
c) the margin of error is decreased?

#### Solution Preview

Please see the attachment for the diagrams and original notations, alongside the solutions posted here below.

*A 90 % confidence interval for a situation is developed and is given by the following 48 < µ < 64.