The maximum number of peaks goes to the left side and a log tail to the right side, so data in sample is positively skewed.
- As, the data is positively skewed so the outliers belongs to the dataset. Thus, in this case the middle vale of the data (Median) will be the most appropriate measure of the center location.
Answer 2
- The null hypothesis for the test is slope is 0 and the alternate hypothesis is slope is different from 0. The t- test will be used to determine whether demand and unit price are related.The calculations are done in excel, the value of the t-test statistic is, -8.61 and the corresponding P-value at 46 degree of freedom and two tailed test is 0.000.
The, P-Value is less than the significance level, so the null hypothesis gets rejected. Hence, it can be conclude that, demand and unit price are related.
- The formula to calculate the coefficient of determination is R-Square =(SSR/SST). The calculations are done in excel. The value of R-Square is 0.6171. So, 61.71% of the variation in demand explained by the unit price in the regression equation.
- The calculation are done in excel, the value of the correlation coefficient between demand and unit price is 0.7856. Thus, the value of correlation coefficient is near to 1, so it can say that there is a strong positive relationship between demand and the unit price, as the unit price increases demand also increases.
Answer 3
The formulas of the completely randomized design is,
Source of variation
|
Sum of squares
|
Degrees of freedom
|
Mean square
|
F-Statistic
|
Between Treatments
|
SSTR
|
k-1
|
SSTR/k-1
|
(SSTR/k-1)/(SSE/n-k)
|
Within Treatments
|
SSE
|
n-k
|
SSE/n-k
|
|
Total
|
SST
|
n-1
|
|
|
The calculations are done in excel, the calculated values are shown below,
Source of variation
|
Sum of squares
|
Degrees of freedom
|
Mean square
|
F-Statistic
|
Between Treatments
|
390.58
|
2
|
195.29
|
25.89
|
Within Treatments
|
158.4
|
21
|
7.54
|
|
Total
|
548.98
|
23
|
|
|
The, P-Value is 0.000. So, the P-value is less than the 5% level of significance. Thus, the null hypothesis of the test gets rejected. Hence, there is statistically significance difference among the means of the three populations.
Answer 4
- The estimated regression equation relating Y to X1 and X2 is
Y= 0.8051+0.4977 (X1) + 0.4733 (X2)
- The null hypothesis for the F-test is, all the slope coefficient is 0. And the alternate hypothesis is, at least one of the slope coefficient is different from 0.
The calculations are done in excel, the value of test statistic is 80.12 and the corresponding P-Value is 0.000. The P-Value is less than the 5% level of significance, so the null hypothesis of the test gets rejected. Hence, there is statistically sufficient evidence to conclude that, there is a significant relationship between all independent variables and dependent variables.
The null hypothesis for the test is slope for X1 is 0 and the alternate hypothesis is slope is different from 0.The calculations are done in excel, the value of the t-test statistic is, 1.078 and the corresponding P-value at 4 degree of freedom and two tailed test is 0.3417.
The, P-Value is greater than the significance level, so the null hypothesis does not gets rejected. Hence, it can be conclude that, slope of X1 is not different from 0.The null hypothesis for the test is slope for X2 is 0 and the alternate hypothesis is slope is different from 0.The calculations are done in excel, the value of the t-test statistic is, 12.23 and the corresponding P-value at 4 degree of freedom and two tailed test is 0.0003.
The, P-Value is less than the significance level, so the null hypothesis gets rejected. Hence, it can be conclude that, slope of X1 is different from 0.The estimated slope for advertising sports is 0.4733, the slope indicates that as the advertising sports increases by 1 the mobile phone sold per day will increases by 0.4733 percentages.
- The calculations are done in excel, About 15 mobile phones that will be sell if company charges $20000 using 10 advertising sports.