Question

A Colonial Colonel wants to know if the average range of the cannon has decreased. Historically, this average has been 1000 feet. From a random sample of 30 cannon fires (i.e., 30 cannon shots), the average distance was 987 feet with a sample standard deviation of 55 feet. Assume α = 0.05 and that the population is normally distributed. Complete a Hypothesis Test - all steps (including defining mu, Null and Alternative Hypotheses; calculate test statistic and p-value; formalize the decision, conclusion, and any interpretations).

Answer 1

H0: = 1000

Ha: < 1000

Test statistics

t = - / S / sqrt(n)

= 987 - 1000 / 55 / sqrt(30)

= -1.29

From T table,

With test statistics -1.29 and df of 29,

p-value = 0.1036

Decision - Since p-value > 0.05 level, we do not have sufficient evidence to reject H0.

Conclusion - We conclude at 0.05 level that we fail to support the claim that average range of the

cannon has decreased.