Question

A sample of size =n62 is drawn from a normal population whose standard deviation is =σ8.8 The sample mean is=x44.69

(a) Construct a 95% confidence interval for μ Round the answer to at least two decimal places.

A 95% confidence interval for the mean is

<μ<

.

(b) If the population were not approximately normal, would the confidence interval constructed in part (a) be valid? Explain.

The confidence interval constructed in part (a) (would or would not) be valid since the sample size ( is or is not) large

  

.

Answer 1

sample mean 'x̄=	44.690
sample size    n=	62.00
std deviation σ=	8.800
std error ='σx=σ/√n=	1.1176

for 95 % CI value of z=		1.960
margin of error E=z*std error =		2.19
lower bound=sample mean-E=		42.4995
Upper bound=sample mean+E=		46.8805
from above 95% confidence interval for population mean =(42.50 <μ< 46.88)

b)The confidence interval constructed in part (a)  

would be valid since the sample size is  large (>30)