Question

Assume that lengths of newborn babies follow a normal distribution with mean μ. The lengths (in centimeters) of seven randomly selected newborn babies are :45、46、59、53、46、51、54

(give answer to TWO places past decimal)

1. Construct a 99% confidence interval for μ: Lower Bound?, Upper Bound: ？

2. Perform a hypothesis test to see if the population mean length is more than 50 centimeters (HA : μ > 50) at the significant level α = 0.05:

Compute the test statistic:_____

Indicate the rejection region
t > t_0.025,6
t > t_0.05,6
t > t_0.05,7
t > t_0.025,7

Is there enough evidence to reject the Null hypothesis (H₀: μ = 50)?
Yes, reject.
No, don't reject.

Answer 1

from the data we can easily calculate

sample size =n=7

sample mean=m=50.57

sample SD=S=5.19

a)

we have sample SD hence we will use t statistics with DF=n-1=7-1=6

now 99% confidence interval is given by

so interval is (41.97,59.17)

b)

we have to test

now test statistics is given by

t have df=n-1=7-1=6

P-Value =P(t>0.29)=0.3908

t critical is given by

P(t> critical Value )=0.05

critical value= t(0.05,6)

from t table P(t>1.943)=0.05

Hence we reject H0 if

t > t0.05,6

since P-Value is more than level of significance hence we failed to reject H0

Hence No, don't reject.