Question

5. Calculate the minimum required sample size. a. See number 3 above. 6. Given a set of ordered pair data calculate the correlation coefficient. r. calculate and interpret the coefficient of determination find the equation of the regression line, and make a prediction. a. Listed below are the budgets (in millions of dollars) and the gross receipts (in millions of dollars) for randomly selected movies. Construct a scatterplot find the value of the linear correlation coefficient r, and find the P-value using a=0.05. Budget 62 88 50 31 201 99 89 Gross 62 63 48 61 146 46 ii. Is there sufficient evidence to conclude that there is a linear correlation between budgets and gross receipts? Do the results change if the actual budgets listed $62,000, $88,000, $50,000, and so on? 1. What are the null and alternative hypotheses? 2. Identify the linear coefficient r. 3. Identify the test statistic 4. Identify the P-value. 5. What is the conclusion based on the hypothesis test? 6. What is the conclusion based on the confidence interval?! 7. What is the significance of the coefficient of determination 7. Use the five-step approach of hypothesis testing to verify claims about linear correlation, and one two sample means and proportions. a. See number 4.c above.

Answer 1

6. (a) The scatterplot is:

Gross HHHHHHH + + + + ++ + + + ++ + + ++ + + ++ + +日 / 50 100 150 200 250 Budget

The output is:

	r²	0.853
	r	0.924
	Std. Error	78.138
	n	7
	k	1
	Dep. Var.	Gross
ANOVA table
Source	SS	df	MS	F	p-value
Regression	1,77,287.3737	1	1,77,287.3737	29.04	.0030
Residual	30,527.4835	5	6,105.4967
Total	2,07,814.8571	6
Regression output					confidence interval
variables	coefficients	std. error	t (df=5)	p-value	95% lower	95% upper
Intercept	-135.8573
Budget	3.1161	0.5783	5.389	.0030	1.6296	4.6026

1. The hypothesis being tested is:

H₀: There is no relationship between the Budget and Gross.

H_a: There is a relationship between the Budget and Gross.

2. r = 0.924

3. t = 5.389

4. p-value = 0.0030

5. Since the p-value (0.0030) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we have sufficient evidence to conclude that there is a relationship between the Budget and Gross.

6. From the 95% confidence interval, we have sufficient evidence to conclude that there is a relationship between the Budget and Gross.

7. r² = 0.853

It means that 85.3% of the variability in Gross is explained by the Budget.

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