Question

A horticulturist working for a large plant nursery is conducting experiments on the growth rate of a new shrub. Based on previous research, the horticulturist feels the average weekly growth rate of the new shrub is 3cm per week. A random sample of 45 shrubs has an average growth of 1.50cm per week with a standard deviation of 3cm. Is there overwhelming evidence to support the claim that the growth rate of the new shrub is less than 3cm per week at a 0.050 significance level?

Find the value of the test statistic. Round your answer to three decimal places, if necessary.

Answer 1

Test statistic = - 3.354

We reject H0 and conclude that the growth rate of the new shrub is less than 3cm per week.

Explanation:

H0 : μ = 3

H1 : μ < 3

The test statistic = (xbar - μ) / (s/ √n)

Xbar = 1.50

μ = 3

s = 3

n = 45

Test statistic = (1.5 - 3) / (3/ √45)

Test statistic = - 1.5 / 0.4472135

Test statistic = - 3.354

Pvalue, using the Pvalue from Z score calculator :

Pvalue = 0.00039826

α = 0.05

Pvalue < α ; We reject H0 and conclude that the growth rate of the new shrub is less than 3cm per week.