Question

Fernanda runs a large bowling league. She suspects that the league average score isgreater than 155 per game. She takes a random sample of 40 game scores from theleague data. The scores in the sample have a mean of 158 and a standard deviation of30. Fernanda wants to use these sample data to conduct a t-test on the mean. Assumethat all conditions for inference have been met. Calculate the t-test statistic.Answer the following:a. (1 pt) population mean,b. (1 pt) sample mean, Xc. (1 pt) sample standard error, sxd. (1 pt) sample size, ne. (2 pts) calculate the t-test statistic​

a. (1 pt) Population mean

b. (1 pt) Sample mean, X

c. (1 pt) Sample standard error, s

d. (1 pt) Sample size, n

Answer 1

The population mean is greater than 155. The sample mean is 158. The sample standard error is 4.743. The sample size is 40. The t-test statistic is 0.633.

Step-by-step explanation:

a. Population mean: The population mean is the average score for all games in the league. Since Fernanda suspects that the league average score is greater than 155 per game, the population mean is greater than 155.

b. Sample mean, X: The sample mean is the average score of the 40 game scores in the random sample. In this case, the sample mean is 158.

c. Sample standard error, s: The sample standard error is calculated by dividing the sample standard deviation by the square root of the sample size. In this case, the sample standard error is 30 / sqrt(40) = 4.743.

d. Sample size, n: The sample size is the number of game scores in the random sample. In this case, the sample size is 40.

e. T-test statistic: The t-test statistic is calculated by subtracting the population mean from the sample mean, and then dividing that difference by the sample standard error. In this case, the t-test statistic is (158 - 155) / 4.743 = 0.633.