Ageyser is a hot spring that periodically erupts a mixture of hot water and steam. old faithful in yellowstone national park is the world's most famous geyser. is is suspected that there is a correlation between the duration of the eruptions and the wait time between eruptions. open the data file oldfaithful. use this information to answer questions 1 through 6.

1. fill in the missing variables in the equation of the linear regression line used to predict the wait time between eruptions by the duration of each eruption. (round your answers to three decimal places, example: 23.456)
haty =+x
2. give a 95% confidence interval for the slope of the regression line obtained when duration is used to predict wait time. (round your answers to three decimal places, example: 23.445)
(, )
3. using software, predict the wait time between eruptions following a 6 minute eruption. give your answer accurate to 1 decimal place. (example: 80.4)
y =
conduct a hypothesis test using this information to see if there is a statistically significant linear relationship between the duration of the eruptions and the wait time between eruptions. use a level of significance of alpha = 0.05 .
4. choose the correct null and alternative hypotheses for this analysis.
h_o: b_0 = 0qquadh_a: b_0 ! = 0
h_o: b_1 = 0qquadh_a: b_1 ! = 0
h_o: beta_0 = 0 qquadh_a: beta_0 ! = 0
h_o: beta_1 = 0 qquadh_a: beta_1 ! = 0
5. give the value of the test statistic and the p-value. (round your answers to three decimal places, example: 0.567)
t=
p-value ~~
6. what decision do you make based on the p-value and the level of significance (alpha), and, thus, what do you conclude?
fail to reject the null. there is sufficient evidence to suggest that the slope of the true linear regression line does not equal zero. we conclude that there is not a linear relationship between the duration of eruptions and the wait time between eruptions.
fail to reject the null. there is insufficient evidence to suggest that the slope of the true linear regression line does not equal zero. we conclude that there is not a linear relationship between the duration of eruptions and the wait time between eruptions.
reject the null. there is sufficient evidence to suggest that the slope of the true linear regression line does not equal zero. we conclude that there is a linear relationship between the duration of eruptions and the wait time between eruptions.
reject the null. there is insufficient evidence to suggest that that the the slope of the true linear regression line does not equal zero. we conclude that there is a linear relationship between the duration of eruptions and the wait time between eruptions.