Question

Determine the mean and standard deviation of your sample. Find the 80%, 95%, and 99% confidence intervals. Make sure to list the margin of error for the 80%, 95%, and 99% confidence interval. Create your own confidence interval (you cannot use 80%, 95%, and 99%) and make sure to show your work. Make sure to list the margin of error. What trend do you see takes place to the confidence interval as the confidence level rises? Explain mathematically why that takes place. Provide a sentence for each confidence interval created in part c) which explains what the confidence interval means in context of the topic of your data

WV 49.6 OH 39.2 NE 3.1 NH 34 MD 32.2 ME 29.9 MA 28.2 KY 27.9 DE 27.8 CT 27.7 RI 26.9 NJ 22 MI 21.2 PA 21.2 VT 20 NC 19.8 TN 19.3 IN 18.8 IL 17.2 WI 16.9 NM 16.7 MO 16.5 FL 16.3 NY 16.1 SC 15.5 UT 15.5 VA 14.8 AK 13.9 AZ 13.5 NV 13.3 OK 10.2 CO 10 GA 9.7 WA 9.6 LA 9.3 AL 9 WY 8.7 OR 8.1 MN 7.8 IA 6.9 AR 6.5 MS 6.4 ID 6.2 CA 5.3 KS 5.1 TX 5.1 ND 4.8 SD 4.0 MT 3.6 HI 3.4

Answer 1

Mean and standard deviation

The mean and standard deviation values are obtained in excel using the function =AVERAGE() and STDEV(). The screenshot is shown below,

80%, 95%, and 99% confidence intervals.

80% confidence intervals.

The confidence interval for the mean is obtained using the formula,

where the margin of error is,

From the data values,

Sample mean = 15.8940

Sample standard deviation = 10.2845

The t critical value is obtained from t distribution table for significance level = 0.20 and degree of freedom = n -1 = 50 - 1 = 49.

Now, the margin of error value is,

and

95% confidence intervals.

The t critical value is obtained from t distribution table for significance level = 0.05 and degree of freedom = n -1 = 50 - 1 = 49.

Now, the margin of error value is,

and

99% confidence intervals.

The t critical value is obtained from t distribution table for significance level = 0.01 and degree of freedom = n -1 = 50 - 1 = 49.

Now, the margin of error value is,

and

Additionally,

90% confidence intervals.

The t critical value is obtained from t distribution table for significance level = 0.10 and degree of freedom = n -1 = 50 - 1 = 49.

Now, the margin of error value is,

and

Conclusion:

The calculated confidence intervals are,

	Lower Limit	Upper Limit
80% CI	13.9656	17.8224
90% CI	13.4053	18.3827
95% CI	12.9109	18.8771
99% CI	11.9158	19.8722

We can see that as the significance level is decreasing, the confidence interval gets wider. This is because the margin of error value is increasing due to the increase in the value of t critical value.

As the significance level is decreasing we are getting more confident that the true populating mean will lie in this interval.