A company is developing a new high performance wax for cross country ski racing.

Question

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 The champion's times (selected at random) are 57.9, 60.1, 51.8, 51.8, 48.2,45.2, 52.8, and 43.7D seconds to complete the test course. Should they market the wax? Assume the assumptions and conditions for appropriate hypothesis testing are met for the sample. Assume a = 0.05. Choose the correct null and alternative hypotheses below. H_0:mu > 55 H_0:mu = 55 H_A:mu = 55 H_A:mu

Explanation / Answer

a)      Correct alternative:

B. H0: µ = 55 versus Ha: µ < 55

Test statistic value = t = -1.7649

P-value = 0.0605

Correct conclusion

D) No, do not market the wax as there is insufficient evidence to conclude the mean time is less than 55 seconds.

t Test for Hypothesis of the Mean

Data

Null Hypothesis                m=

55

Level of Significance

0.05

Sample Size

8

Sample Mean

51.4375

Sample Standard Deviation

5.709375122

Intermediate Calculations

Standard Error of the Mean

2.0186

Degrees of Freedom

7

t Test Statistic

-1.7649

Lower-Tail Test

Lower Critical Value

-1.8946

p-Value

0.0605

Do not reject the null hypothesis

b)      Correct alternative: B

They had made a type I error and will lose the potential profit from selling the wax.

(Type I error is defined as the probability of rejecting the null hypothesis even it is true.)

t Test for Hypothesis of the Mean

Data

Null Hypothesis                m=

55

Level of Significance

0.05

Sample Size

8

Sample Mean

51.4375

Sample Standard Deviation

5.709375122

Intermediate Calculations

Standard Error of the Mean

2.0186

Degrees of Freedom

7

t Test Statistic

-1.7649

Lower-Tail Test

Lower Critical Value

-1.8946

p-Value

0.0605

Do not reject the null hypothesis

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