Use the listed paired sample data, and assume that the...

Use the listed paired sample data, and assume that the samples are simple random samples and that the differences have a distribution that is approximately normal. Listed below are "attractiveness" ratings made by participants in a speed dating session. Each attribute rating is the sum of the ratings of five attributes (sincerity, intelligence, fun, ambition, shared interests). The listed ratings are from Data Set 18 "Speed Dating." Use a 0.05 significance level to test the claim that there is a difference between female attractiveness ratings and male attractiveness ratings. $$\begin{array}{|l|l|l|l|l|l|l|l|l|l|l|l|l|} \hline \text { Rating of Male by Female } & 4.0 & 8.0 & 7.0 & 7.0 & 6.0 & 8.0 & 6.0 & 4.0 & 2.0 & 5.0 & 9.5 & 7.0 \\ \hline \text { Rating of Female by Male } & 6.0 & 8.0 & 7.0 & 9.0 & 5.0 & 7.0 & 5.0 & 4.0 & 6.0 & 8.0 & 6.0 & 5.0 \\ \hline \end{array}$$

Use the listed paired sample data, and assume that the samples are simple random samples and that the differences have a distribution that is approximately normal.
Listed below are "attractiveness" ratings made by participants in a speed dating session. Each attribute rating is the sum of the ratings of five attributes (sincerity, intelligence, fun, ambition, shared interests). The listed ratings are from Data Set 18 "Speed Dating." Use a 0.05 significance level to test the claim that there is a difference between female attractiveness ratings and male attractiveness ratings.
$$\begin{array}{|l|l|l|l|l|l|l|l|l|l|l|l|l|}
\hline \text { Rating of Male by Female } & 4.0 & 8.0 & 7.0 & 7.0 & 6.0 & 8.0 & 6.0 & 4.0 & 2.0 & 5.0 & 9.5 & 7.0 \\
\hline \text { Rating of Female by Male } & 6.0 & 8.0 & 7.0 & 9.0 & 5.0 & 7.0 & 5.0 & 4.0 & 6.0 & 8.0 & 6.0 & 5.0 \\
\hline
\end{array}$$

Key Concepts

Paired Samples

This refers to situations where data consists of two sets of related observations, typically from the same subjects or matched conditions, allowing for the analysis of differences within each pair instead of comparing independent groups.

Hypothesis Testing

This is a systematic procedure for testing a claim about a population parameter. It involves setting up a null hypothesis (usually stating no difference or effect) and an alternative hypothesis (stating that there is a difference or effect) and then using sample data to determine which hypothesis is more consistent with the observed results.

Paired t-Test

The paired t-test is a statistical method used to compare the means of two related groups. It calculates the differences within each pair and assesses whether the average of these differences is significantly different from zero, assuming the differences are normally distributed.

Normality Assumption

This assumption implies that the differences between paired observations follow a normal distribution. It is a crucial condition for the validity of many statistical tests, including the paired t-test, especially when the sample size is small.

Significance Level

The significance level, often denoted as alpha (?), is the threshold for deciding whether an observed effect is statistically significant. A common significance level of 0.05 indicates a 5% risk of rejecting the null hypothesis incorrectly when it is actually true.

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