1. Consider a sample of size 50 from a population with unknown mean. (5.5 pts) a

Question

1.               Consider a sample of size 50 from a population with unknown mean. (5.5 pts) a) Suppose you know the standard deviation of the population. Would you use values of z or t to construct a confidence interval for µ? Afterwards find either the z or t value needed to construct the intervals with the following confidence levels. i. 95% ii. 99% iii. 94% iv. 93%

b)     Suppose you do not know the standard deviation of the population. Would you use values of z or t to construct a confidence interval for µ? Afterwards find either the z or t value needed to construct the intervals with the following confidence levels. i. 95% ii. 99% iii. 80%

Explanation / Answer

1) AS WE KNOW STD deviation, we will use z distribution

below is the value of z corresponding to confidence levels

(i) 95% ---1.96

(ii) 99%--2.5758

(iii)94%---1.8808

(iv)93% ---1.8119

b) for unknown std deviation we should use t distribution

here degree of freedom =n-1=49

i)95% ---2.010

(ii)99%---2.68

(iii)80%---1.299

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