Question

Determine if there is sufficient evidence to conclude the average amount of divorces is less than or equal to 4000 in the United States and territories at the 0.10 level of significance. N=52

1. Clearly state a null and alternative hypothesis
2. Give the value of the test statistic
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.

Summary Table for Divorces
Mean	1,399
Median	1,176
Standard Deviation	1407
Minimum	0
Maximum	7,008

Answer 1

Given that, sample size = 52

sample mean = 1399 and standard deviation = 1407

The null and alternative hypotheses are,

H0 : μ = 4000

Ha : μ < 4000

Test statistic is,

=> Test statistic = z = -13.33

p-value = P(Z < -13.33) = 0

=> p-value = 0

Since, p-value = 0 is less than 0.10 level of significance, we reject the null hypothesis.

Conclusion : There is sufficient evidence to conclude the average amount of divorces is less than or equal to 4000 in the United States and territories at the 0.10 level of significance.