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. 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 company wants the mean time $\mu$ to be less than 55 seconds. The null hypothesis $H_0$ is a statement of no - effect or equality, and the alternative hypothesis $H_A$ is what we are trying to find evidence for. So, $H_0:\mu = 55$ and $H_A:\mu<55$.
Step2: Recall the formula for the one - sample t - statistic
The formula for the one - sample t - 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 the sample size $n = 8$ in this part of the problem, we can't calculate the t - statistic for now. However, for the hypothesis selection part, the correct answer is based on the logic of hypothesis testing for a one - sided (left - tailed) test.
Answer:
B. $H_0:\mu = 55$, $H_A:\mu<55$