Question

The distribution of newborn Golden Retriever puppy weights is known to be approximately normal. Twenty-four newborn retriever pups were weighed. The sample mean was 389.4 grams. The sample standard deviation was 19.3 grams.

a) Construct a 90% confidence interval for the mean weight of newborn Golden Retriever puppies. Write a complete sentence describing the meaning of this confidence interval.

b) What happens to the confidence interval if the sample size increases to 30 pups? Explain.

Answer 1

a)Only sample information are given ,we will use t statistic to caculate confidence interval .

xbar +/- t (s/ sqrt(n))

Crtical value for df = n-1= 24-1=23 at aplha=0.10 is

t=1.714 ( from t table)

90% Confidence interval

389.4 +/- (1.714) (19.3/sqrt (24))

389.4 +/- (6.752)

Or (382.648 396.152 )

Meaning - in repeated sampling, if we calculate confidence intervals then 90% of confidence intervals will contain the true population mean.

B) form formula of confidence interval we can see, as n increases, confidence interval will decreases.So when n= 30 confidence interval will decrease accordingly in respect of n=24