Your friend decided to enroll in a reading course that allegedly increases reading speed and comprehension. Prior to enrolling in the elass your friend read 198 words per minute (wpm). The following data represent the words per minute read for 10 different passages read after the course.
$\begin{array}{lllll}206 & 217 & 197 & 199 & 210 \\ 210 & 197 & 212 & 227 & 209\end{array}$
Was the class effective? In other words, test the claim that your friend's reading rate is now greater than 198 wpm using the $\alpha=0.05$ level of significance. Note: the normal probability plot and boxplot show that the reading rates are approximately normal without outliers.
State the null and alternative hypothesis. Input " $> $ " or " $< $ " or "=" to complete the alternative.
Test statistic. Round to 4 decimals:
P-value. Round to 4 decimals:
Conclusion: There is
evidence at the level of significance to conclude that your friend's reading rate is ("equal to" or "greater than"
or "less than" or "not equal to")
198 wpm.

Step 1 ：State the null and alternative hypothesis. The null hypothesis is that the reading rate is equal to 198 wpm, and the alternative hypothesis is that the reading rate is greater than 198 wpm.

Step 2 ：Calculate the test statistic and the p-value. The test statistic is calculated as the difference between the sample mean and the hypothesized population mean, divided by the standard error of the sample mean. The p-value is the probability of observing a test statistic as extreme as, or more extreme than, the observed test statistic, under the null hypothesis.

Step 3 ：Compare the p-value to the level of significance. If the p-value is less than the level of significance, we reject the null hypothesis and conclude that the reading rate is greater than 198 wpm. If the p-value is greater than the level of significance, we do not reject the null hypothesis and conclude that the reading rate is equal to 198 wpm.

Step 4 ：The test statistic is approximately \(\boxed{3.5049}\) and the p-value is approximately \(\boxed{0.0033}\). Since the p-value is less than the level of significance (0.05), we reject the null hypothesis.

Step 5 ：Therefore, there is evidence at the 0.05 level of significance to conclude that your friend's reading rate is greater than 198 wpm.

Step 6 ：Final Answer: Null hypothesis: The reading rate is equal to 198 wpm. Alternative hypothesis: The reading rate is greater than 198 wpm. Test statistic: \(\boxed{3.5049}\) P-value: \(\boxed{0.0033}\) Conclusion: There is evidence at the 0.05 level of significance to conclude that your friend's reading rate is \(\boxed{\text{greater than}}\) 198 wpm.