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The attribute ratings given by participants in a speed dating session are provided.

It is claimed that there is a difference between male attribute ratings and female attribute ratings.

Null Hypothesis: The mean of the differences between male and female attribute ratings is equal to 0.

\({H_0}:{\mu _d} = 0\)

Alternative Hypothesis: The mean of the differences between male and female attribute ratings is not equal to 0.

\({H_1}:{\mu _d} \ne 0\)

The differences between male and female attribute ratings are tabulated below:

The mean of the differences is computed below:

\(\begin{array}{c}\overline d = \frac{{\sum\limits_{i = 1}^n {{d_i}} }}{n}\\ = \frac{{\left( { - 7} \right) + 4 + ...... + 1}}{9}\\ = 1.89\end{array}\)

The standard deviation of the differences is computed below:

\(\begin{array}{c}{s_d} = \sqrt {\frac{{\sum\limits_{i = 1}^n {{{({d_i} - \overline d )}^2}} }}{{n - 1}}} \\ = \sqrt {\frac{{{{\left( {\left( { - 7} \right) - 1.89} \right)}^2} + {{\left( {4 - 1.89} \right)}^2} + ....... + {{\left( {1 - 1.89} \right)}^2}}}{{9 - 1}}} \\ = 7.15\end{array}\)

Thus, the mean and the standard deviation of the differences are 1.89 and 7.15, respectively.

The assumption from the null hypothesis states that \({\mu _d} = 0\).

Then, the test statistic value is computed below:

\(\begin{array}{c}t = \frac{{\overline d - {\mu _d}}}{{\frac{{{s_d}}}{{\sqrt n }}}}\\ = \frac{{1.89 - 0}}{{\frac{{7.15}}{{\sqrt 9 }}}}\\ = 0.793\end{array}\)

Thus, the value of t is equal to 0.793.

The value of the degrees of freedom is computed below:

\(\begin{array}{c}df = n - 1\\ = 9 - 1\\ = 8\end{array}\)

Using the t-distribution table, the critical values oft for 8 degrees of freedom and at a 0.05 level of significance are -2.306 and 2.306.

The two-tailed p-value of the z-score equal to 0.739 is equal to 0.4810.

Since the test statistic value lies within the two critical values and the p-value is greater than 0.05, the null hypothesis is failed to reject.

There is insufficient evidence to support the claim that there is a difference between female attribute ratings and male attribute ratings.