Statistics Assignment - Desklib

This Statistics Assignment covers topics like Hypothesis Testing, Regression Analysis. It includes solutions to problems related to testing hypotheses, calculating p-values, correlation coefficient, regression coefficients, and more. The assignment is suitable for students pursuing courses in Statistics, Mathematics, and related fields. The University and Course Code are not mentioned.

Running Head: STATISTICS ASSIGNMENT
Statistics Assignment
Name of the Student
Name of the University
Author Note

1STATISTICS ASSIGNMENT
Table of Contents
Answer 1..........................................................................................................................................2
Answer 2..........................................................................................................................................3
Answer 3..........................................................................................................................................4
Answer 4..........................................................................................................................................5

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Answer 1
Hypothesized mean mass of all bags (μ) = 50 kg
Sample mean mass of bags ( X ) = 48.18 kg
Standard deviation of the sample masses ( σ ) = 3 kg
Sample size (n) = 10 bags
Degrees of freedom = 9
Type of test = Upper tail test
(a) To test at 1% level of significance, whether the mean mass of the bags is less than
50 kg, the following hypothesis can be framed:
H0 : μ≥ 50
Against H A : μ<50
The test statistic to test the above hypothesis can be given as follows:
tObserved= X −μ
σ
√ n
¿ 48.18−50
3
√10
¿−1.918
The critical value of t with 9 degrees of freedom at 1% level of significance ( tCritical ) =
2.8214. Thus, tObserved < tCritical. Hence, null hypothesis ( H0) is accepted. Thus, Mr. Rutter
cannot conclude that the mean mass of the bags is less than 50 kg.
(b) The p-value is given by P ( Z <tObserved ) =P ( Z ←1.918 ) =0.02743

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Answer 2
Hypothesized mean rate of credit card debt (μ) = 14
Sample mean rate of credit card deb ( X ) = 15.64
Standard deviation of the sample rates ( σ ) = 1.561
Sample size (n) = 10
Degrees of freedom = 9
Type of test = Lower tail test
tCritical at 1% level of significance = – 2.8214
To test at 1% level of significance, whether the mean rate of credit card debt is greater
than 14%, the following hypothesis can be framed:
H0 : μ≤ 14
Against H A : μ>14
The test statistic to test the above hypothesis can be given as follows:
tObserved= X −μ
σ
√n
¿ 15.64−14
1.561
√ 10
¿ 3.3223

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Thus, tObserved > tCritical. Hence, null hypothesis (H0) is accepted. Thus, it is reasonable to conclude
that the mean rate charged is greater than 14%.
Answer 3
Population proportion of staffs and shoppers using public transportation (P) = 0.5
Sample size = 1002
Number of people using public transportation = 483
Sample proportion ( ^p )= 483
1002=0.48
Type of test = Two tailed test.
ZCritical at 5% level of significance = 1.96
To test whether the proportion of staffs and shoppers using public transportation have changed,
the following null and alternate hypothesis can be framed:
H0 : P=0.5
Against H A : P ≠ 0.5
The test statistic to test the above hypothesis can be given as follows:
ZObserved = ^p−P
√ P(1−P)
n
¿ 0.48−0.5
√ 0.5 ×0.5
1002

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¿−1.1373
Thus, ZObserved < ZCritical. Hence, null hypothesis (H0) is accepted. Thus, it is reasonable to
conclude that the survey results do not indicate a change.
Answer 4
(a) The scatter diagram showing the relationship between the age and the selling
price is given in figure 4.1
5 6 7 8 9 10 11 12 13
0
2
4
6
8
10
12
Scatter Diagram
Age (Years)
Selling Price ($ '000's)
Figure 4.1: Scatter Diagram
(b) Here, mean of age ( X ) = 109
12 =9.08
Average selling price ( Y ) =82.90
12 =6.91
The correlation coefficient between age of the car and its selling price is:
r xy= ∑ xy−∑ x ∑ y
√∑ x2
∑ y2 =728.90−(109× 82.90)
√1037 ×615.29 =−0.54

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Thus, there is a moderately negative relationship between age and selling price. This
result is not surprising as with the increase in age of a car, the functionality of the car will
decrease and thus, the selling price will also decrease.
(c) The coefficient of determination between age and selling price is
r2=(−0.54)2 =0.29. This measure indicates that 29 percent of the variability in the selling
price of the car can be explained by its age.
(d) To test whether there is a linear relationship between the variables age and its
selling price, the following hypothesis can be framed:
H0 : β=0
Against H A : β ≠0
Here, β is the regression coefficient. From the regression analysis, it can be seen that,
β ≠ 0 and the result is significant at 5% level of significance. Thus, there exists a linear
relationship between age and selling price.
Table 4.1: Regression Coefficients
Coefficient
s
Standard
Error t Stat P-value Lower 95%
Upper
95%
Intercept 11.58 2.36 4.91 0.00 6.32 16.83
Age (years) [X] - 0.51 0.25 -2.03 0.07 -1.08 0.05
(e) The regression equation that can be given to estimate the selling price of the car
based on its age is
Selling Price=11.58−(0.51 × Age)
(f) Here, the value of b (slope of the regression equation) is – 0.51. This indicates
that with the increase in age of the car by 1 year, the selling price of the car decreases by
0.51.

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(g) The estimated selling price of a 10-year-old car is:
Selling Price=11.58− ( 0.51× 10 )=6.44
Therefore, the required estimated selling price of a 10-year old car is $6,440