Question

Sample Size: 52

1. 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.
2. Determine if there is sufficient evidence to conclude the average amount of deaths is equal to 6000 in the United States and territories at the 0.10 level of significance.
3. Determine if there is sufficient evidence to conclude the average amount of marriages is greater or equal to 2500 in the United States and territories at the .05 level of significance.
4. 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.

• clearly state a null and alternative hypothesis
• Give the value of the test statistic
• Report the P-Value
• Clearly state your conclusion (Reject the Null or Fail to Reject the Null)
• Explain what your conclusion means in context of the data.

LIVE BIRTHS

Mean	6911
Median	4750
Standard Deviation	8161.31
Minimum	582
Maximum	46,424

DEATHS

Mean	3958
Median	2964
Standard Deviation	4039.60
Minimum	280
Maximum	19,767

MARRIAGES

Mean	3876
Median	2792
Standard deviation	4424.42
Minimum	215
Maximum	21,368

DIVORCES

Mean	1587
Median	1340
Standard Deviation	1427.25
Minimum	98
Maximum	6400

Answer 1

The null and alternative hypothesis are:

The null hypothesis, Ho: µ ≤ 5000.

The average amount of deaths is less than or equal to 5000.

Alternative hypothesis, H1: µ > 5000.

The average amount of deaths is more than 5000.

Give the value of the test statistic.

We are given with:

Sample mean, x = 3877.19

Standard Deviation, s = 3950.91

Significance level, α = 0.10

Sample size, n = 52

Degree of freedom, df = n - 1 = 52 – 1 = 51

Test statistic, t = (x - µ)/s/ Ön

                        = (3877.19– 5000)/3950.91/Ö52

                     = (-2122.81)/3950.91/Ö52

                       = - 3.874

Report the P-Value.

P-value with df= 51 and test statistic = -3.874 at α = 0.10 is, 0.0002.

Clearly state your conclusion (Reject the Null or Fail to Reject the Null)

Since the p-value is less than the significance level, we can reject the null hypothesis. 0.0002<0.10.

Explain what your conclusion means in context of the data.

Therefore, we have insufficient evidence to conclude the average amount of deaths is less than or equal to 5000.