Question

A e site isted the battery lfe (in hors and uminous intensity screen Click the icon to view the technology oupt trees in cd m" or в sa ple of tablet computers Researchers want to kno it screen b htness is associated m banery ife Use the technology output en bel 10 ans er oar s a) through g a) How many teblet computers were tested? Technology Outout b) Are the condtions for interence tise? Explain. Select al cond tions for inference that are satisied Dependent variable Video battery lfe in hours) R-squared-4 62 1.974 with 69-2 67 degrees of freedom A. Tha nesidual plot and tscamarpiot shaw consistent variablity B. The scattarplot of the data is roughty linear with lots of scatter C. Normal probabity plot of residuals 15 reasonably straight. D. The plot of the residuals looks random. E. None of the assumplons and condiions for inference are salsfed Varlable Coetticient SE(Coat) t-ratio P-value Intercept 6.10194 0.9543 647 0.0000 Brightness 0.00474 0.0023 179 0.0780 c) ls there evidence of an assccietion betaeen maximum brightness of the screen and bettery life? Test an appropriste hypothesis and ste your concusion using a 005 level of sgnificance State the null and altemative hypothes0s a, O A. Ho Thane is no inear relationship between brigntness and batery ife HA . Then t; a negative reationship batwaan hnghtness and hattery tta, fil «o B. H0 There is no linear relationship between brightness and battery life. :0. HA: There is & Inear relañionship between brightness and bettery ife, p O C. Ho- There is a linear relationship beween brightness and balitery lie p 0. HA. There is no inear relsionship between brightuness and battery ie p10 Print Done O D. Ho There ts no inear relationchip between brigntness and bathery lte P-D HA: There ts postrve relationship between bnghtness and battery ite, β1 > Determine hetest statistic Roune to two decimal places as needed) Find the P-value. P-value (Round to four decimal places as needed) State the conclusion. O A. Fall to reject Ho. These data do not provide evildence of a pos tive lineer relatlonshlp beween brigess and bmery ife O D. Reect Ho. These dala provide evidence of aposilve inear relonship between brightess and bttery fe. С. Rc;ect HU These data do not provide evidence at postrve incar relationship between brightness and battery life O D. Fall to rejct Ho These dara provide evicence of a positve Inear reletionship between brightmess and battery ig d) Is the association strong? Explain. Choose the correct answer below. A. No, the association s not strong, because the value of R-squared is on 4 6 %. This low value of R-squared, and the high value o s 1.974 indicate at most of the vanation is not explaned by his regression. О В Yes, the association is strong, because the value of squared is 4.62%. This high value of-squared, and the low value of s 1 974 ndicate that most ofthe variation se plained this regression. C No, the association is not strong because the value o R squared is 4 62%. This high value of R squared, and the i value ofs, 1 974 indicate that most o the vanation se plained by his gre on D. Yes he association is strong, because he value o R-squared is only 4 %. This low value o Rsquared, and the ngh value o s l 4 indicate na most of the va a s to pained by ns ress on e) What is the equation of the regression line? Hours-| - | × Screen Brightness Round to five decimal places as needed.) f) Create a 95% confidence interval for the slope of the true line OD A 95% confidence interval for β1 is Round to five decimal places as needed.) g) Interpret your interval in this context O A Luminous intensity increases on average, by an amount between the upper and over limits of he confidence inter a per increase in battery if one hour with 9 % B. With 95% confidence, the predicted value of battery life will be between the upper and lower limits of the confidence interval when the value of brightness is known. n dence. .. An increase in battery life by one hour will cause an increase in brightness by a number of cd/m2 between the upper and lower limits of the confidence interval with a 95% probability. D. Battery life increases, on average, by an amount between the upper and lower limits ofthe confidence interval per increase in brightness of one cd/m. with 95% confidence.

Answer 1

From the output the df is n-2=69-2=67.

So we can say that 69 tablet computers were tested.

b) From the model adequacy plot we can say that:

The scatter plot is roughly linear with lot of scatters

The plot of residual is not random

Normal probability plot is reasonably straight.

The Scatter plot and residual plot shows consistent variability

c) To test the significance of slope we have Option A

Ha : Biメ0

t= 1.77

The p value =0.0813

since the p value is > 0.05 we fail to reject H₀ (Option A)

d) Option C) The association is not strong beacause the R squared value is only 4.93% and s=1.911 the low value of R and high value of s indicate that the most of the variation is not explained by the regression.

The fitted line is

battery life = 6.06104 + 0.0047 * brightness

f ) The slope CI is sample statistic + margin of error

The sample statistic is the slope coefficient 0.00477

margin of error = critical value * standard error

critical value= 0.975 at 95 % level

standard error=0.0023

margin of error=0.975*0.0023= 0.0022425

CI = 0.00477 + 0.0022425

( 0.0025275 , 0.0070125)

Interpretation is correctly given in Option A