ZZ. Case 112 A company I\'d developing a new high- performance wax for cross cou
ID: 3153230 • Letter: Z
Question
ZZ. Case 112 A company I'd 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 satandard test course should be less than 55 seconds for a former Olympic champion. To test it, the champion will ski the course 8 times. The champion's times ( selected at random) are 59.7, 60.4, 51.8 51.8, 47.8, 47.6, 54.7, and 44.8 seconds to complete the test course.A. What is the value of the test statistic? Round to two decimal places B. What is the P-value of the test statistics? Round to three decimal places. C. Should they market the wax? 1. No, there is sufficient evidence to conclude the mean time is less than 55 seconds 2. No, there is insufficient evidence to conclude the mean time is less than 55 seconds. 3. Yes, there is sufficient evidence to conclude the mean time is less than 55 seconds. 4. Yes, there is insufficient evidence to conclude the mean time is less than 55 seconds
D. Suppose they decide not to market the wax after the test, but it turns out that the wax really does lower the champion's average time to less than 55 seconds. What kind of error have they made? Explain the impact of such an error 1. They made a Type II error and will lose the potential profit from selling the wax. 2. They made a Type II error and customers might demand their money back. 3. They made a Type I error and will lose the potential profit from selling the wax. 4. They made a Type I error and customers might demand their money back.
ZZ. Case 112 A company I'd 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 satandard test course should be less than 55 seconds for a former Olympic champion. To test it, the champion will ski the course 8 times. The champion's times ( selected at random) are 59.7, 60.4, 51.8 51.8, 47.8, 47.6, 54.7, and 44.8 seconds to complete the test course.
A. What is the value of the test statistic? Round to two decimal places B. What is the P-value of the test statistics? Round to three decimal places. C. Should they market the wax? 1. No, there is sufficient evidence to conclude the mean time is less than 55 seconds 2. No, there is insufficient evidence to conclude the mean time is less than 55 seconds. 3. Yes, there is sufficient evidence to conclude the mean time is less than 55 seconds. 4. Yes, there is insufficient evidence to conclude the mean time is less than 55 seconds
D. Suppose they decide not to market the wax after the test, but it turns out that the wax really does lower the champion's average time to less than 55 seconds. What kind of error have they made? Explain the impact of such an error 1. They made a Type II error and will lose the potential profit from selling the wax. 2. They made a Type II error and customers might demand their money back. 3. They made a Type I error and will lose the potential profit from selling the wax. 4. They made a Type I error and customers might demand their money back.
A company I'd 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 satandard test course should be less than 55 seconds for a former Olympic champion. To test it, the champion will ski the course 8 times. The champion's times ( selected at random) are 59.7, 60.4, 51.8 51.8, 47.8, 47.6, 54.7, and 44.8 seconds to complete the test course.
A. What is the value of the test statistic? Round to two decimal places B. What is the P-value of the test statistics? Round to three decimal places. C. Should they market the wax? 1. No, there is sufficient evidence to conclude the mean time is less than 55 seconds 2. No, there is insufficient evidence to conclude the mean time is less than 55 seconds. 3. Yes, there is sufficient evidence to conclude the mean time is less than 55 seconds. 4. Yes, there is insufficient evidence to conclude the mean time is less than 55 seconds
D. Suppose they decide not to market the wax after the test, but it turns out that the wax really does lower the champion's average time to less than 55 seconds. What kind of error have they made? Explain the impact of such an error 1. They made a Type II error and will lose the potential profit from selling the wax. 2. They made a Type II error and customers might demand their money back. 3. They made a Type I error and will lose the potential profit from selling the wax. 4. They made a Type I error and customers might demand their money back.
Explanation / Answer
A) THE H0 = U =55
Ha= u<55
alpha = 0.05
HERE NOW WE NEED TO FIND THE MEAN AND STANDARD DEVIATION
t test = (52.32 - 55)/(5.67/sqrt(8)) = -1.34
b) p value for t = -1.34
degree of freedom = 8-1 = 7
alpha = 0.05
it comes out to be = 0.1110
c) as the p value if insignificant therefore we will reject the null hypothesis
therefore option C is correct
d) it is like a case fail to reject the false null hypothesis
hence type 2 error
and option A is correct
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