Questions: You ask a group of 10 adults to participate in a reaction time task concerning verbal comprehension while under the influence of a computer-simulated virtual reality system stimulating the retina of one of a participant's eyes. Our collected data follows: Completion time in seconds 0.8 1.1 0.7 0.9 1.0 0.9 1.1 1.2 1.4 0.8 See alpha at a = .05 and summarize the results of the hypothesis testing procedure by writing your results in normal form as suggested in the image.

Solution Steps

The sample mean \( \mu \) is calculated as follows:

\[ \mu = \frac{\sum_{i=1}^N x_i}{N} = \frac{9.9}{10} = 0.99 \]

The sample variance \( \sigma^2 \) is computed using the formula:

\[ \sigma^2 = \frac{\sum (x_i - \mu)^2}{n-1} = 0.05 \]

The standard deviation \( \sigma \) is then:

\[ \sigma = \sqrt{0.05} = 0.21 \]

The standard error \( SE \) is calculated as:

\[ SE = \frac{\sigma}{\sqrt{n}} = \frac{0.21}{\sqrt{10}} \approx 0.0664 \]

The test statistic \( t \) is calculated using the formula:

\[ t = \frac{\bar{x} - \mu_0}{SE} = \frac{0.99 - 1.0}{0.0664} \approx -0.1506 \]

For a two-tailed test, the p-value \( P \) is given by:

\[ P = 2 \times (1 - T(|z|)) \approx 0.8836 \]

Since the p-value \( 0.8836 \) is greater than the significance level \( \alpha = 0.05 \), we fail to reject the null hypothesis. This indicates that there is no significant difference in the mean completion time.

Final Answer