Question

What is the relationship between the number of minutes per day a woman spends talking on the phone and the woman's weight? The time on the phone and weight for 9 women are shown in the table below. 28 15 Time Pounds 68 149 22 100 64 124 57 143 67 141 101 77 126 68 127 100 0 a. Find the correlation coefficient: r = Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: Ho: ? H:? 0 The p-value is: (Round to four decimal places) c. Use a level of significance of a = 0.05 to state the conclusion of the hypothesis test in the context of the study. There is statistically significant evidence to conclude that there is a correlation between the time women spend on the phone and their weight. Thus, the regression line is useful There is statistically insignificant evidence to conclude that there is a correlation between the time women spend on the phone and their weight. Thus, the use of the regression line is not appropriate. There is statistically insignificant evidence to conclude that a woman who spends more time on the phone will weigh more than a woman who spends less time on the phone. There is statistically significant evidence to conclude that a woman who spends more time on the phone will weigh more than a woman who spends less time on the phone. d. 2 (Round to two decimal places) e. Interpretr?: O 70% of all women will have the average weight. There is a 70% chance that the regression line will be a good predictor for women's weight based on their time spent on the phone. Given any group of women who all weight the same amount, 70% of all of these women will weigh the predicted amount. There is a large variation in women's weight, but if you only look at women with a fixed weight, this variation on average is reduced by 70% f. The equation of the linear regression line is: (Please show your answers to two decimal places) . Use the model to predict the weight of a woman who spends 34 minutes on the phone. Weight - (Please round your answer to the nearest whole number.)

Answer 1

S.No х Y 1 2 3 4 5 6 7 8 9 Total 68 28 22 15 64 57 67 68 77 466 149 101 100 100 124 143 141 127 126 1111 123.4444 (x-x) 263.1605 565.3827 886.7160 1352.6049 149.3827 27.2716 231.7160 263.1605 636.1605 4375.5556 SSX (y-7) 653.09 503.75 549.64 549.64 0.31 382.42 308.20 12.64 6.53 2966.2222 (x-x)(y-7) 414.5679 533.6790 698.1235 862.2346 6.7901 102.1235 267.2346 57.6790 64.4568 3006.8889 Mean 51.778 SSY SXY sample size n. 9 4375.556 S 51.7778 y = 123.4444 SO (X-X) = S. (x-2)(y-7)= slope= . 5./5.- intercept= B. - V-B.X= 3006.889 0.6872 Cov 87.8627

a)

correlation r='Sxy/(√Sxx*Syy) =

0.8346

b_)

null hypothesis: Ho:           ρ'=		0
Alternate Hypothesis: Ha: ρ≠		0

test stat t=	r*(√(n-2)/(1-r2))=	4.0092
P value    =	0.0051	(from excel:tdist(4.009,7,2)

c)

There is statistically significant evidence to conclude that there is a correlation between the time women spend on the phone and their weight. Thus, the regression line is useful.

d_)

Coefficient of determination R2=0.70

e)

There is a large variation in women's weight, but if you only look at women with a fixed weight, this variation on average is reduced by 70%.

f)

Least square line equation: ŷ =87.86+0.69*x

g)

predicted val=87.86+34*0.69=

111

h)

For every additional minute women spend on the phone, they tend to weigh on averge 0.69 additional pounds.

i)

The best prediction for the weight of a woman who does not spend any time talking on the phone is 88 pounds.