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.

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