Question

4. The mean weight of newborn infants at a community hospital is 6.6 pounds A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. Do they really weigh only 6.6 pounds? I thought they would weigh more.

A. State the hypotheses

b. Find the calculated value of the test statistic

c. State critical value at α = .05

d. State conclusion

Answer 1

A) Null and alternative hypotheses

Ho : = 6.6

Ha : > 6.6

B) Test statistic

t = ( xbar - )/(s/√n)

t = (7.56 - 6.6)/(1.18/√7)

t = 2.15

C) critical value for a = 0.05 , d.f = n -1 = 6

tCritical = t​​​​​​a ,n-1 = t​​​​​​0.05, 6

tCritical = 1.94

D) Decision rule : if t > 1.94 we reject the null hypothesis otherwise we fail to reject the null hypothesis

Our t = 2.15 > 1.94

Conclusion : Reject the null hypothesis Ho . There is sufficient evidence to support the claim that the mean weight of newborn infants at community hospital is more than 6.6 pounds