Question

When to use a Confidence interval vs a p-value?

How do I find the Confidence interval using Z*?

I have values for r, SE, s, and sample size. Also Z* for 80, 90, 95, 98, 99%

please explain formulas/calculations and info, Thank You

Answer 1

We can use either P values or confidence intervals to determine whether your results are statistically significant. If a hypothesis test produces both, these results will agree.

The confidence level is equivalent to 1 – the alpha level. So, if your significance level is 0.05, the corresponding confidence level is 95%.

• If the P value is less than your significance (alpha) level, the hypothesis test is statistically significant.
• If the confidence interval does not contain the null hypothesis value, the results are statistically significant.
• If the P value is less than alpha, the confidence interval will not contain the null hypothesis value.

Confidence Interval with the z distribution

If you don’t know your population mean (μ) but you do know the standard deviation (σ), you can find a confidence interval for the population mean, with the formula:
x̄ ± z* σ / (√n),

Let us take an example:

Sample problem: Construct a 95 % confidence interval an experiment that found the sample mean temperature for a certain city in August was 101.82, with a population standard deviation of 1.2. There were 6 samples in this experiment.

Step 1: Subtract the confidence level (Given as 95 percent in the question) from 1 and then divide the result by two. This is your alpha level, which represents the area in one tail.
(1 – .95) / 2 = .025

Step 2: Subtract your result from Step 1 from 1 and then look that area up in the middle of the z-table to get the z-score:

1. 1 – 0.025 = 0.975
2. z score = 1.96.

Step 3: Plug the numbers into the second part of the formula and solve:
z* σ / (√n)
= 1.96 * 1.2/√(6)
= 1.96 * 0.49
= 0.96

Step 4: For the lower end of the range, subtract step 3 from the mean.
101.82 – 0.96 = 100.86

Step 5: For the upper end of the range, add step 3 to the mean.
101.82 + 0.96 = 102.78.

The CI is (100.86,102.78)

The Z value for

Confidence Level	z*– value
80%	1.28
85%	1.44
90%	1.64
95%	1.96
98%	2.33
99%	2.58