Question

A study of bone density on 5 random women at a hospital produced the following result. Suppose a significance level of a=0.02 to perform this hypothesis test. Age 33 Bone density 340 37 335 45 330 65 325 73 310 a. Draw a scatter plot of the data. b. Calculate Test- Statistic the significance of the correlation coefficient c. State the null and alternative hypothesis? d. Calculate the p-value? e. Do you reject or fail you reject the null hypothesis? f.At the level of significance, from the sample data, there (is/is not) Sufficient evidence --- -- between --- and g. Use regression to find the equation for the line of best fit and describe the correlation (Positive correlation, Negative correlation, or Zero Correlation) h. Find the Linear Regression equation. 1. What is the best-predicted value for y given x = 4?

Answer 1

(a) The plot is:

(b) The test statistic, t = -4.968

(c) The hypothesis being tested is:

H₀: = 0

H_a: ≠ 0

(d) The p-value is 0.0157.

	r²	0.892
	r	-0.944
	Std. Error	4.376
	n	5
	k	1
	Dep. Var.	Bone density
ANOVA table
Source	SS	df	MS	F	p-value
Regression	472.5518	1	472.5518	24.68	.0157
Residual	57.4482	3	19.1494
Total	530.0000	4
Regression output				confidence interval
variables	coefficients	std. error	t (df=3)	p-value	95% lower	95% upper
Intercept	359.2973
Age	-0.6185	0.1245	-4.968	.0157	-1.0148	-0.2223