Use the following to answer questions 21-24:
A landscaping company hypothesizes that the median number of lawns they mow in a weekend is 20. They tabulated the number of lawns mowed in a random sample of 14 weekends. = .05), taken from Table J in the text:
-What is the test value?
A) 3
B) 4
C) 7
D) 8

Question

Use the following to answer questions 21-24:
A landscaping company hypothesizes that the median number of lawns they mow in a weekend is 20. They tabulated the number of lawns mowed in a random sample of 14 weekends.  = .05), taken from Table J in the text: 
-What is the test value?
A) 3 
B) 4 
C) 7 
D) 8

Quizplus · Accepted Answer

To find the test value, we use the formula:
(test statistic) = (sample statistic - hypothesized parameter) / (standard error)
Here, the sample median is 18 and the hypothesized median is 20.
The standard error can be calculated as: 
standard deviation / sqrt(sample size)
We do not have the standard deviation, but we can estimate it using the sample data.
The median is a resistant measure of center, so we can use the median absolute deviation (MAD) as an estimate of the standard deviation. 
MAD = median of the absolute deviations from the median = median(|x_i - median|) = 3
So, the standard error = 3 / sqrt(14) = 0.802
Plugging in the values, we get:
(test statistic) = (18 - 20) / 0.802 = -2.49 (rounded to two decimal places)
Using Table J from the text, the corresponding p-value is 0.013.
Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is evidence to suggest that the median number of lawns mowed in a weekend is less than 20.
The test statistic value is -2.49, which is closest to option A) 3.

Use the Following to Answer Questions 21-24