Mathematics A) Spreadsheet Data Analysis B) State

Mathematics

a) Spreadsheet Data Analysis

b) State hypotheses:

Ho: Type of soft drink and resident are independent. (null hypothesis)

Ha: Type of soft drink and resident are not independent. (alternate hypothesis)

c) Conduct chi-square test of independence at 0.05 significance level: = 0.05

d) Calculate degrees of freedom: Number of rows = 2, Number of columns = 2

Degrees of freedom (df) = (Number of rows - 1) x (Number of columns - 1) = (2-1)(2-1) = 1

e) Calculate the expected frequencies from actual data:

f) Calculate the chi-square statistic using both actual and expected frequency tables:

In excel, the cursor was placed in cell M17 and the formula of chi test typed as:

=CHITEST (actual frequency range, expected frequency range)

=CHITEST (L4:M5, L13:M14), as shown in the formula bar above

The result gives, the calculated chi-square probability, p = 1.2203 x 10-10

g) Look up the Chi-Square value, ?2 from chi-square distribution tables for df = 1 and ? = 0.05

2 = 3.84 from tables

h) Now we need to check whether or not the calculated chi-square probability, p is less than or equal to ? = 0.05 OR the Chi-Square value, ?2 from chi-square distribution tables is equal to or greater than ? = 0.05. If p OR ?2, we reject the null hypothesis and conclude that at the 0.05 significance level, there is a relationship between the row variables and column variables. Since p = 1.2203 x 10-10 < ? = 0.05 (OR ?2 = 3.84 > ? = 0.05) we conclude that there is a relationship between type of soft drink and resident response.

2. a) Forbes Data

Based on the statistical report and values highlighted, we see that there is a significant relationship between:

i) sales and market value, ii) sales and cash flow, iii) cash flow and market value

The rest indicates that there is no significant relationship between the remaining pairs of different variables.

We now perform a multiple regression analysis assuming sales as the dependent variable, with market value and cash flow as independent variables. The hypotheses for this test is stated as:

Ho: slope of the regression line = 0. (null hypothesis)

Ha: slope of the regression line ? 0. (alternate hypothesis)

We choose significance level = 0.05 and reject the null hypothesis if p-value < 0.05

Given that the p-values suggest otherwise, we may conclude that, there exists enough evidence at ? = 0.05 to conclude that the slope of the regression line is not zero and, that market value and cash flow (independent variables) are useful joint predictors of sales (dependent variable). However, we may also say that the cash flow is a more useful predictor of sales than the market value, given the relatively small p-value of market value.

Quiz and Homework Dataset2

FLSA PTFT Status YOS Age Union Salary EType FTE Ethnic Gender PR06 PR07

1 1-1-2.70-30.00 2-52,000 1-1 1-1-3 3

1 1-1-12.20-43.00 2-94,800 1-1 1-1-3 3