Questions: For an experiment testing the pineapple gummy bear, our alternative hypothesis would state "There is a difference in a taster's ability to identify the flavor of the pineapple gummy bear based on taste and smell and taster alone". If our alternative hypothesis is supported what would we expect the results of our experiment to show The number of correct responses in the control group and the treatment group to be similar. The number of correct responses does not determine if the alternative hypothesis is supported or not. The number of correct responses in the control group to be greater than the number of correct responses in the treatment group.

Solution Steps

The Standard Error \( (SE) \) is calculated using the formula:

\[ SE = \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}} = \sqrt{\frac{1.3444}{10} + \frac{1.1667}{10}} = 0.5011 \]

The test statistic \( (t) \) is computed as follows:

\[ t = \frac{\bar{x}_1 - \bar{x}_2}{SE} = \frac{6.3 - 8.5}{0.5011} = -4.3903 \]

The degrees of freedom \( (df) \) are calculated using the formula:

\[ df = \frac{\left(\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}\right)^2}{\frac{\left(\frac{s_1^2}{n_1}\right)^2}{n_1 - 1} + \frac{\left(\frac{s_2^2}{n_2}\right)^2}{n_2 - 1}} = \frac{0.0631}{0.0035} = 17.9102 \]

The p-value \( (P) \) is calculated as:

\[ P = 2(1 - T(|t|)) = 2(1 - T(4.3903)) = 0.0004 \]

Given that the p-value \( (0.0004) \) is less than the significance level \( (\alpha = 0.05) \), we reject the null hypothesis. This supports the alternative hypothesis, indicating that there is a difference in a taster's ability to identify the flavor of the pineapple gummy bear based on taste and smell and taster alone.

Final Answer