Absentee rates - Friday vs Wednesday: We want to test whether or not more students are absent on Friday afternoon classes than on Wednesday afternoon classes. In a random sample of 292 students with Friday afternoon classes, 58 missed the class. In a different random sample of 307 students with Wednesday afternoon classes, 34 missed the class. The table below summarizes this information. The standard error (SE) is given to save calculation time if you are not using software.

Data:

	total number	total number	Proportion of
Day	of absences (x)	of students (n)	p
Friday	58	292	0.19863
Wednesday	34	307	0.11075

SE = 0.02947

The Test: Test the claim that the absentee rate on all Friday afternoon classes is greater than the absentee rate on all Wednesday afternoon classes. Use a 0.05 significance level. (a) Letting p₁ be the absentee rate from the sample on Friday and p₂ be the rate from Wednesday, calculate the test statistic using software or the formula

z =

(p₁ p₂) _p

SE

where _p is the hypothesized difference in proportions from the null hypothesis and the standard error (SE) given with the data. Round your answer to 2 decimal places. z = (b) What is the P-value of the test statistic? Use the answer found in the z-table or round to 4 decimal places. P-value = (c) What is the critical value of z? Use the answer found in the z-table or round to 3 decimal places. z = (d) What is the conclusion regarding the null hypothesis? reject H₀

fail to reject H₀

(e) Choose the appropriate concluding statement. The data supports the claim that the absentee rate on all Friday afternoon classes is greater than the absentee rate on all Wednesday afternoon classes.

There is not enough data to support the claim that the absentee rate on all Friday afternoon classes is greater than the absentee rate on all Wednesday afternoon classes.

We have proven that the absentee rate on all Friday afternoon classes is greater than the absentee rate on all Wednesday afternoon classes.

We reject the claim that the absentee rate on all Friday afternoon classes is greater than the absentee rate on all Wednesday afternoon classes.

Wait-Times: There are three registers at the local grocery store. I suspect the mean wait-times for the registers are different. The sample data is depicted below. The second table displays results from an ANOVA test on this data with software.

Wait-Times in Minutes

									x
Register 1	2.0	2.0	1.1	2.0	1.0	2.0	1.0	1.3	1.55
Register 2	1.8	2.0	2.2	2.6	1.8	2.1	2.2	1.7	2.05
Register 3	2.1	2.1	1.8	1.5	1.4	1.4	2.0	1.7	1.75

ANOVA Results

F	P-value
3.669	0.0430

The Test: Complete the steps in testing the claim that there is a difference in mean wait-times between the registers.

(a) What is the null hypothesis for this test? H₀: ₂ > ₃ > ₁.H₀: _{1 2 3}.

H₀: ₁ = ₂ = ₃.H₀:

At least one of the population means is different from the others.

(b) What is the alternate hypothesis for this test? H₁: At least one of the population means is different from the others.

H₁: _{1 2 3}.

H₁: ₁ = ₂ = ₃.H₁: ₂ > ₃ > ₁.

(c) What is the conclusion regarding the null hypothesis at the 0.10 significance level? reject H₀

fail to reject H₀

(d) Choose the appropriate concluding statement. We have proven that all of the mean wait-times are the same.

There is sufficient evidence to conclude that the mean wait-times are different.

There is not enough evidence to conclude that the mean wait-times are different.

(e) Does your conclusion change at the 0.05 significance level? Yes

No

Below is the scatterplot, regression line, and corresponding statistics for Advertising Expenditures (in thousands of dollars) and Sales (in thousands of dollars) from a selection of8months.

Advertising -vs- Sales: x= Advertising Expenses (in thousands of dollars) y= Sales (in thousands of dollars) correlation coefficient: r=0.964 regression equation: =13.99x+93.4 sample size: n=8

Answer the following questions regarding the relationship between Advertising Expenditures (x) and Sales (y).(a) What is the slope of the regression equation? 93.4

8

13.99

0.964 (b) With respect to the variables involved, choose the best interpretation of the slope of the regression equation. For every one thousand dollar increase in Sales, you can expect to spend 13.99 thousandlessdollars on Advertising.

For every one thousand dollar increase in Advertising Expenditures, you can expect sales todecreaseby 13.99 thousand dollars.

For every one thousand dollar increase in Advertising Expenditures, you can expect sales toincreaseby 13.99 thousand dollars.

For every one thousand dollar increase in Sales, you can expect to spend 13.99 thousandmoredollars on Advertising.