# Statistical Analysis: Confidence Interval Determination

1. In a study designed to test the effectiveness of magnets for treating back pain, 40 patients were given a treatment with magnets and also a sham treatment without magnets. Pain was measured using a scale 0(no pain) to 100 (extreme pain). After given the magnet treatments, the 40 patients had pain scores with a mean of 10.0 and a standard deviation of 2.5. After being given the sham treatments, the 40 patients had pain scores with a mean of 8.3 and a standard deviation of 2.2.

a. Construct the 95% confidence interval estimate of the mean pain score for patients given the magnet treatment.

What is the confidence interval estimate of the population mean µ?

___ < µ <____

b. Construct the 95% confidence interval estimate of the mean pain score for patients given the sham treatment.

What is the confidence interval estimate of the population mean µ?

___ < µ <____

c. Compare the results. Does the treatment with magnets appear to be effective?

2. The eruption height and time interval after eruption of a geyser were measured and are shown below. (graph attached)

Height (x) 150 110 125 120 125 140 120 140

Interval after (y) 87 65 40 94 101 92 94 55

a. Find the value of the linear correlation coefficient r.

R=___

b. Find the critical values of r from the table showing critical values for the Pearson correlation using α=0.05.

The critical values are ±

c. Is there sufficient evidence to conclude that there is a linear correlation between the two variables?

3. a. Write a correct alternative hypothesis for: Ho: µ ≤ 35.

b. Answer "True" if the statement is always true. If the statement is not always true, replace the underlined words with words that make the statement always true.

1 − α is known as the level of significance of a hypothesis test

4. Find the critical z values. Assume that the normal distribution applies. Two-tailed test; α=0.09

z=_____

5. Find the P-value. Also use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis)

The test statistic in a left-tailed test z=-1.56

What is the P-value?

P-value=____

https://brainmass.com/statistics/descriptive-statistics/statistical-analysis-confidence-interval-determination-550617

#### Solution Summary

The solution gives detailed steps on solving 5 statistical problems using normally distributed data such as finding confidence intervals, finding z-score and finding p-value. All formula and calculations are shown and explained.