To obtain a 3 percent margin of error at a 90 percent level of confidence requires a sample size of about 750. For a 95 percent level of confidence, the sample size would be about 1,000. Determining the margin of error at various levels of confidence is easy.

Example 11 Find the minimum sample size required to estimate the proportion to within three percentage points, at 90% confidence. Solution: Confidence level 90% means that α=1−0.90=0.10 so α∕2=0.05.

Because you want a 95% confidence interval, your z*-value is 1.96. Take the square root to get 0.0499. The margin of error is, therefore, plus or minus 1.96 ∗ 0.0499 = 0.0978, or 9.78%….How to Determine the Confidence Interval for a Population Proportion.

1.96

Checking Out Statistical Confidence Interval Critical Values

Therefore, a z-interval can be used to calculate the confidence interval.

1. Step 1: Go to the z-interval on the calculator. Press [STAT]->Calc->7.
2. Step 2: Highlight STATS. Since we have statistics for the sample already calculated, we will highlight STATS at the top.
3. Step 3: Enter Data.
4. Step 4: Calculate and interpret.

You need to input a confidence level in the margin of error calculator….How to calculate margin of error.

A 95% confidence interval is a range of values (upper and lower) that you can be 95% certain contains the true mean of the population.

In statistics, critical value is the measurement statisticians use to calculate the margin of error within a set of data and is expressed as: Critical probability (p*) = 1 – (Alpha / 2), where Alpha is equal to 1 – (the confidence level / 100).

In hypothesis testing, a critical value is a point on the test distribution that is compared to the test statistic to determine whether to reject the null hypothesis. If the absolute value of your test statistic is greater than the critical value, you can declare statistical significance and reject the null hypothesis.

Think of the mean as a “mirror”. We know that the critical value at the mean is zero. Every critical value to the left of the mean is negative. Every critical value to the right of the mean is positive.

If the level of significance is α = 0.10, then for a one tailed test the critical region is below z = -1.28 or above z = 1.28. For a two tailed test, use α/2 = 0.05 and the critical region is below z = -1.645 and above z = 1.645.

A critical region, also known as the rejection region, is a set of values for the test statistic for which the null hypothesis is rejected. i.e. if the observed test statistic is in the critical region then we reject the null hypothesis and accept the alternative hypothesis.

H0: The null hypothesis: It is a statement of no difference between sample means or proportions or no difference between a sample mean or proportion and a population mean or proportion. In other words, the difference equals 0….An appropriate alternative hypothesis is:

1. p = 0.20.
2. p > 0.20.
3. p < 0.20.
4. p ≤ 0.20.

To find the significance level, subtract the number shown from one. For example, a value of “. 01” means that there is a 99% (1-. 01=.

The significance level, also denoted as alpha or α, is the probability of rejecting the null hypothesis when it is true. For example, a significance level of 0.05 indicates a 5% risk of concluding that a difference exists when there is no actual difference.

1. Data Set-Up. Your data should include two variables (represented in columns) that will be used in the analysis.
2. Run an Independent Samples t Test. To run an Independent Samples t Test in SPSS, click Analyze > Compare Means > Independent-Samples T Test.
3. Example: Independent samples T test when variances are not equal.