plain type fonts such as times new roman are easier to rean than fancy fonts such as gigi. a group of 25 voulunteer subjects read the same text in both fonts. (this is a matched pairs design. One-sample procedures for proportions, like those for means, are used to analyze data from matched pairs designs.) of the 25 subjects, 17 said that they preferred times new roman for web use. but 20 said that gigi was more attractive

To analyze the data from the matched pairs design and compare the proportions, you can use one-sample procedures for proportions. Let's break down the steps:

Step 1: Define the null and alternative hypotheses.
- Null hypothesis (H0): There is no difference in preference between Times New Roman and Gigi fonts for web use.
- Alternative hypothesis (Ha): There is a difference in preference between Times New Roman and Gigi fonts for web use.

Step 2: Conduct the statistical analysis.
- You have a sample size of 25 volunteers who read the same text in both fonts.
- Out of the 25 subjects, 17 preferred Times New Roman for web use, while 20 preferred Gigi.
- To analyze the data, you can use a one-sample proportion test. This test compares the observed proportion (p) to a hypothesized proportion (p0) specified in the null hypothesis.

Step 3: Calculate the test statistic.
- Calculate the observed proportion (p) of subjects who preferred Times New Roman: p = 17/25 = 0.68.
- Calculate the hypothesized proportion (p0) specified in the null hypothesis (50% since there is no difference assumed): p0 = 0.50.
- Calculate the standard error (SE) of the proportion: SE = sqrt(p0 * (1 - p0) / n) = sqrt(0.50 * 0.50 / 25) = 0.10.
- Calculate the test statistic (z-score): z = (p - p0) / SE = (0.68 - 0.50) / 0.10 = 1.8.

Step 4: Determine the critical value and p-value.
- The critical value for a two-sided test at a significance level of 0.05 is approximately ±1.96 (from a standard normal distribution table).
- Calculate the p-value associated with the observed test statistic using a standard normal distribution table or statistical software. The p-value represents the probability of obtaining a test statistic as extreme as, or more extreme than, the observed value, assuming the null hypothesis is true.

Step 5: Make a conclusion.
- If the observed test statistic falls within the critical region (outside the range defined by the critical values), the null hypothesis is rejected in favor of the alternative hypothesis.
- Alternatively, if the p-value is less than the chosen significance level (usually 0.05), the null hypothesis is rejected.

Note: The analysis for the preference of Gigi font can be done using the same steps, replacing the proportions and calculating another z-score.

Keep in mind that it's essential to use appropriate statistical software or consult a statistician to perform these calculations accurately.