Understanding Basic Statistics 6th Edition by Charles Henry Brase,Corrinne Pellillo Brase

Exercise 38

For all Hypothesis tests, please provide the following information:
(i) What is the level of significance State the null and alternate hypotheses.
(ii) Check Requirements What sampling distribution will you use What assumptions are you making What is the value of the sample test statistic
(iii) Find (or estimate) the P -value. Sketch the sampling distribution and show the area corresponding to the P -value.
(iv) Based on your answers in parts (i)-(iii), will you reject or fail to reject the null hypothesis Are the data statistically significant at level
(v) Interpret your conclusion in the context of the application.
Inferences for Linear Regression Plate tectonics and the spread of the ocean floor are very important in modern studies of earthquakes and earth science in general. A random sample of islands in the Indian Ocean gave the following information, where x = age of a volcanic island in the Indian Ocean (units in 10 6 years) and y = distance of the island from the center of the midoceanic ridge (units in 100 km).

x = 415; y = 128; x 2 = 30,203 y 2 = 2558.5; xy = 8133.
(a) Verify that the standard error of estimate S e 6.50.
(b) Verify that the sample correlation coefficient r 6.50. Use a 5% level of significance to test that is positive.
(c) Verify that the equation of the least-squares line is
. Use a 5% level of significance to test that is positive.
(d) Given that the age of a volcanic island is 55 (units 10 6 years), predict how far the island is from the center of the midoceanic ridge (units in 100 km). Find an 85% confidence interval for the prediction.