Question

A certain variety of rosebush is known to produce a large number of rose blooms during the blooming period. Bob jr is a botanist that knows this particular rosebush usually produces 75 roses per rosebush during the blooming season. However, he experience tells him that this figure may be wrong and need to be re-evaluated. He selects 32 of these rosebushes and finds that on average they produce 78 roses during the blooming season with a standard deviation of 12 roses. With ? = 0.05, test Bob jr's claim that the average number of roses produced by a single rosebush is different from 75 roses.

a. Are you going to use the ?-value or traditional method?

b. Build the hypotheses and find the critical value(s), if needed.  

c. Find the test statistic and the ?-value, if needed.

d. Determine whether the null hypothesis is rejected or not rejected.

e. Summarize your results within the context of the problem.

Answer 1

Answer)

A)

P-value method.

B)

Null hypothesis Ho : u = 75.

alternate hypothesis Ha : u not equal to 75.

C)

Test statistics t = (sample mean - claimed mean)/(s.d/√n).

t = (78 - 75)/(12/√32) = 1.414

Degrees of freedom is = n-1 = 31.

For 31 dof and 1.414 test statistics, P-value from t distribution is 0.1673

D)

Since the obtained P-value is greater than the given significance 0.05.

We fail to reject the null hypothesis Ho.

E)

There is insufficient evidence to support the claim that u is not equal to 75.

D)