At a certain university, the average attendance at basketball games has been 1,000 spectators per game. Due to the dismal showing of the team this year, the attendance for the first four games has been only 700
Spectators per game with a standard deviation of 200.The athletic director claims that the attendance is
The same as last year.If , what is the test statistic?
A)-3.00
B)-6.00
C)-7.00
D)-9.00

Question

At a certain university, the average attendance at basketball games has been 1,000 spectators per game. Due to the dismal showing of the team this year, the attendance for the first four games has been only 700
Spectators per game with a standard deviation of 200.The athletic director claims that the attendance is
The same as last year.If  , what is the test statistic?
A)-3.00 
B)-6.00 
C)-7.00 
D)-9.00

Quizplus · Accepted Answer

We can calculate the test statistic using the formula:

t = (x̄ - μ) / (s / √n)

where x̄ is the sample mean (700), μ is the hypothesized population mean (1000), s is the sample standard deviation (200), and n is the sample size (4). Plugging in the values, we get:

t = (700 - 1000) / (200 / √4) = -300 / 100 = -3.00

Thus, the test statistic is -3.00. The best choice is A. We can use a one-sample t-test to compare the current attendance to last year's average attendance. The null hypothesis is that the current attendance is the same as last year's attendance, and the alternative hypothesis is that the current attendance is less than last year's attendance.

The test statistic can be calculated as:

t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))

Plugging in the values given:

t = (700 - 1000) / (200 / sqrt(4)) = -300 / 100 = -3

Since the alternative hypothesis is that the current attendance is less than last year's attendance, we are looking for a left-tailed test. With 3 degrees of freedom (4 games - 1), the critical value at a significance level of alpha = .05 is -2.920. Since our test statistic (-3.00) is less than the critical value, we reject the null hypothesis and conclude that the current attendance is significantly lower than last year's attendance.

At a Certain University, the Average Attendance at Basketball Games