Question

Determine if there is sufficient evidence to conclude the average amount of births is over 5000 in the United States and territories at the 0.05 level of significance.

Summary Table for Live Births
AVERAGE	6,833
MEDIAN	4,781
STANDARD DEVIATION	8039.02237
MAX	45,231
MIN	537

1. Clearly state a null and alternative hypothesis
2. Give the value of the test statistic n= 52
3. Report the P-Value
4. Clearly state your conclusion (Reject the Null or Fail to Reject the Null)
5. Explain what your conclusion means in context of the data.

Answer 1

Null and alternative hypotheses

Ho : = 5000 ; H1 : > 5000

Test statistic.  

t = (xbar - )/(s/√n)

t = ( 6833- 5000)/(8039.022/√52)

t = 1.64

p-value for t = 1.64 and d.f = n -1 = 51 , right tailed test

p-value = P( t > 1.64) d.f = 51

p-value = 0.0536

Decision rule : if p-value < a we reject the null hypothesis otherwise we fail to reject the null hypothesis

Our p-value = 0.0536 > 0.05

Conclusion : Fail to reject the null hypothesis

There is no sufficient evidence to conclude that the average amount of births is over 5000 in the United States and territories at the 0.05 level of significance.