Question

In: Statistics and Probability

The table below shows the arm spans (in inches) and the heights (in inches) of 10...

The table below shows the arm spans (in inches) and the heights (in inches) of 10 randomly selected people.

Arm Span, x 51 52 56 49 54 59 58 55 52 56
Height, y 51 53 54 50 55 57 58 57 52

56

Perform a test, at the 5% level of significance, for the population slope β 1 of the regression line.

H0:

Ha:

t-Test Statistic (round this value to three decimal places) =

Critical t-Score (t α or t α / 2, use the t-distribution table to find, it should contain three decimal places) =

Conclusion (type R for reject H0, F for fail to reject H0):

Solutions

Expert Solution

The Regression Equation of Y on X is

Wher "r" = Correlation Coefficient

= Mean of X

= Mean of Y

= Standard Deviation of X

= Standard Deviation of Y

X Y
51 51 -3.2 -3.3 10.24 10.89
52 53 -2.2 -1.3 4.84 1.69
56 54 1.8 -0.3 3.24 0.09
49 50 -5.2 -4.3 27.04 18.49
54 55 -0.2 0.7 0.04 0.49
59 57 4.8 2.7 23.04 7.29
58 58 3.8 3.7 14.44 13.69
55 57 0.8 2.7 0.64 7.29
52 52 -2.2 -2.3 4.84 5.29
56 56 1.8 1.7 3.24 2.89
TOTAL 91.6000 68.1000
MEAN 54.2000 54.3000
S.D 3.0265 2.6096
r 0.9167

Therefore the Regression Equation of Y on X is

.

Therefore the fitted Regression Equation of Y on X is  

Here 0.7904 is the slope of the Regression Equation of Y on X which is denoted by

Therefore  

We frame the Null Hypothesis

:

To test the we use the t - Statistic

Therefore

Given α = 5% = 0.05

; So, we Reject at 5% Level of Significant

Therefore we conclude that

NOTE: The critical value of t has been extracted from the tabulated value of t; which posted below.


Related Solutions

The table below shows the arm spans (in inches) and the heights (in inches) of 10...
The table below shows the arm spans (in inches) and the heights (in inches) of 10 randomly selected people. Arm Span, x 51 52 56 49 54 59 58 55 52 56 Height, y 51 53 54 50 55 57 58 57 52 56 1) Construct the 1% confidence interval for the population slope β 1 . Make sure your answers follow the rounding rule in the direction. Lower endpoint = Upper endpoint = 2) Fill in the blanks in...
The table below shows the arm spans (in inches) and the heights (in inches) of 10...
The table below shows the arm spans (in inches) and the heights (in inches) of 10 randomly selected people. Arm Span, x 51 52 56 49 54 59 58 55 52 56 Height, y 51 53 54 50 55 57 58 57 52 56 What is the point estimate for the mean height of all people whose arm span is exactly 53 inches? Make sure your answer follows the rounding rule MUST ROUND TO SIX DECIMAL PLACES
The table below shows the arm spans (in inches) and the heights (in inches) of 10...
The table below shows the arm spans (in inches) and the heights (in inches) of 10 randomly selected people. Arm Span, x 51 52 56 49 54 59 58 55 52 56 Height, y 51 53 54 50 55 57 58 57 52 56 1) Construct the 1% confidence interval for the population slope β 1. Make sure your answers follow the rounding rule in the direction. Lower endpoint = Upper endpoint = 2) Fill in the blanks in the...
For Questions 1-4 , use the table below. It is data for the heights (inches) for...
For Questions 1-4 , use the table below. It is data for the heights (inches) for Ms. Smith’s 4th grade class. Student Height (inches) Student Height (inches) 1 47 11 53 2 47 12 54 3 47 13 55 4 49 14 56 5 50 15 59 6 51 16 59 7 51 17 60 8 52 18 60 9 52 19 60 10 52 20 91 The median height of the students is 42.32 52.50 54.45 58.35 The standard...
Consider the accompanying data examining the heights and arm spans of randomly selected students. Complete parts...
Consider the accompanying data examining the heights and arm spans of randomly selected students. Complete parts a through g below. Height_(cm) Arm_Span_(cm) 179 170 169 179 150 153 175 170 178 153 200 188 161 147 160 151 175 157 173 199 Rsquared=32.6% s=2.56 constant=39.215 height 0.741 a) Write the regression equation. Define the variables used in your equation. Arm Span (cm)=_____+_____•( Height(cm)) b) f a student is 165 cm​ tall, what is his predicted Arm​ Span? c)f this 165...
The following data set shows the heights in inches for the boys in a class of...
The following data set shows the heights in inches for the boys in a class of 20 students. 66; 66; 67; 67; 68; 68; 68; 68; 68; 69; 69; 69; 70; 71; 72; 72; 72; 73; 73; 80 a/ Find the 5-number summary b/Find the interquartile range IQR c/ Are there any outliers? If there are list them d/ Construct a box plot Show Your Work
The following data shows self reported heights and measured heights (in inches) for 8 randomly selected...
The following data shows self reported heights and measured heights (in inches) for 8 randomly selected teenage girls. Is there sufficient evidence, at a 0.05 significance levelto sugest that there is a difference between self reported and measured height? Reported 53,64, 61, 66, 64, 65, 68, 63 Measured 58.1 62.7 61.1 64.8 63.2 66.4 67.6 63.5
(Heights of Presidents since 1900) Listed below are the heights (in inches) of the Presidents who...
(Heights of Presidents since 1900) Listed below are the heights (in inches) of the Presidents who started serving in 20th until today. Assume that these values are sample data from some larger population. 67, 70, 72, 71, 72, 70, 71, 74, 69, 70.5, 72, 75, 71.5   69.5, 73, 74, 74.5, 71.5, 73.5, 72.5 (a) Find Q1 and Q3 (b) Construct a boxplot for the data (c) Find the range (d) Find the standard deviation and variance (e) Assume that the...
(Heights of Presidents since 1900) Listed below are the heights (in inches) of the Presidents who...
(Heights of Presidents since 1900) Listed below are the heights (in inches) of the Presidents who started serving in 20th until today. Assume that these values are sample data from some larger population. 67, 70, 72, 71, 72, 70, 71, 74, 69, 70.5, 72, 75, 71.5,   69.5, 73, 74, 74.5, 71.5, 73.5, 72.5, (a) Find the mean (b) Find the median (c) Find Q1 and Q3 (d) Construct a boxplot for the data (e) Find the range (f) Find the...
Consider the heights (inches) for a simple random sample of ten (10) supermodels listed below: 70,...
Consider the heights (inches) for a simple random sample of ten (10) supermodels listed below: 70, 71, 69.25, 68.5, 69, 70, 71, 70, 70, 69.5 There is a claim that supermodels have heights that have much less variation than the heights of women in the general population. (a) Use a Hypothesis test with a significance level of 0.01 to verify the claim that supermodels have heights with a standard deviation that is less than 2.6 inches. (b) Use the Confidence...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT