Question

The Gilmore daycare claims that they use more than 110 diapers daily. The manager takes a random sample of used diapers use 61 days (2 months) and finds that the sample mean is 108 diapers with a standard deviation of 17.

a) Test at α = 0.06

b) Construct a 90% confidence interval

Answer 1

Ans:

a)

$H_0:\mu \leq 110$

$H_a:\mu> 110$

As,n>=30,we can use normal distribution.

Test statistic:

z=(108-110)/(17/sqrt(61))

z=-0.92

p-value=P(z>-0.92)=0.8210

As,p-value>0.06,we fail to reject the null hypothesis.

There is not sufficient evidence to conclude that they use more than 110 diapers daily.

b)

90% confidence interval for mean

=108+/-1.645*(17/sqrt(61))

=108+/-3.58

=(104.42, 111.58)