a company is developing a new high performance wax for cross country ski racing. in order to justify the…

a company is developing a new high performance wax for cross country ski racing. in order to justify the price marketing wants, the wax needs to be very fast. specifically, the mean time to finish their standard test course should be less than 55 seconds for a former olympic champion. to test it, the champion will ski the course 8 times. complete parts a and b below. complete the test course. should they market the wax? assume the assumptions and conditions for appropriate hypothesis testing are met for the sample. assume α = 0.05. choose the correct null and alternative hypotheses below. a. h0:μ<55 ha:μ = 55 b. h0:μ = 55 ha:μ<55 c. h0:μ = 55 ha:μ>55 d. h0:μ>55 ha:μ = 55 calculate the test statistic. t = (round to two decimal places as needed.)

a company is developing a new high performance wax for cross country ski racing. in order to justify the price marketing wants, the wax needs to be very fast. specifically, the mean time to finish their standard test course should be less than 55 seconds for a former olympic champion. to test it, the champion will ski the course 8 times. complete parts a and b below. complete the test course. should they market the wax? assume the assumptions and conditions for appropriate hypothesis testing are met for the sample. assume α = 0.05. choose the correct null and alternative hypotheses below. a. h0:μ<55 ha:μ = 55 b. h0:μ = 55 ha:μ<55 c. h0:μ = 55 ha:μ>55 d. h0:μ>55 ha:μ = 55 calculate the test statistic. t = (round to two decimal places as needed.)

Answer

Explanation:

Step1: Identify null and alternative hypotheses

The null hypothesis $H_0$ is usually a statement of no - effect or status - quo. Here, the claim is that the mean time $\mu$ to finish the course should be less than 55 seconds. So, $H_0:\mu = 55$ and $H_A:\mu<55$. The correct choice is B.

Step2: Recall the formula for one - sample t - test statistic

The formula for the one - sample t - test statistic is $t=\frac{\bar{x}-\mu_0}{s/\sqrt{n}}$, but since we are not given the sample mean $\bar{x}$, sample standard deviation $s$ and only the hypotheses are asked for in the first part and the test - statistic calculation is incomplete without sample data, we can only state the formula for now.

Answer:

B. $H_0:\mu = 55$, $H_A:\mu<55$ (Note: The value of $t$ cannot be calculated without sample data such as sample mean and sample standard deviation)