A company is developing a newhigh-performance wax for cross country ski racing. In order to justify the price marketingwants, 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 testit, the champion will ski the course 8 times. Thechampion's times are 54.5, 65.5, 48.6, 53.7, 49.2, 45.1, 52.8, and 41.2 seconds to complete the test course. Complete parts a and b below.

a) Should they market thewax? Assume the assumptions and conditions for appropriate hypothesis testing are met for the sample. Assume =0.05. What are the null and alternativehypotheses? Choose the correct answer below.

A. H0: <55 vs. ha: =55

B. H0: =55 vs. HA: <55

C. H0: =55 vs. HA: >55

D. H0: >55 vs. HA: = 55

What is the value of the teststatistic?

The test statistic is __. (Round to two decimal places asneeded.)

What is theP-value of the teststatistic?

P-value= __. (Round to three decimal places asneeded.)

Should they market thewax?

A. No. There is sufficient evidence to conclude the mean time is less than 55 seconds.

B. Yes. There is insufficient evidence to conclude the mean time is less than 55 seconds.

C. Yes. There issufficient evidence to conclude the mean time is less than 55 seconds.

D. No. There isinsufficient evidence to conclude the mean time is less than 55 seconds.

b) Suppose they decide not to market the wax after thetest, but it turns out that the wax really does lower thechampion's average time to less than 55 seconds. What kind of error have theymade? Explain the impact to the company of such an error.

A. They have made a Type II error and customers might demand their money back.

B. They have made a Type I error and customers might demand their money back.

C. They have made a Type II error and will lose the potential profit from selling the wax.

D. They have made a Type I error and will lose the potential profit from selling the wax.

Please show all work. Thank you!