Question

A botanist is interested in determining the average diameter of the flowers of
a particular plant. She decided to take a random sample of size 80 of these
flowers and found that the sample mean of the flower diameters was 9.6 cm,
and the sample standard deviation was 2.2 cm.
(a) Calculate the value of the estimated standard error of the sample mean.
(b) Calculate a 95% confidence interval for the population mean of the
flower diameter of this particular plant.
(c) Interpret the confidence interval from part (b) in terms of all possible
random samples of flowers of this plant.
(d) On the basis of the confidence interval from part (b), what would have
been the outcome of a z-test of the null hypothesis that the population
mean of the flower diameters is 11 cm? Interpret the result of the test

Answer 1

n = 80

sample mean = 9.6

sample sd = 2.2

(a) SE = s /sqrt(n) = 2.2 / sqrt(9.6) = 0.246

(b) 95% CI

t value = TINV ( 0.05, 79) = 1.990

E = t * SE = 1.990 * 0.246 = 0.490

CI = mean +/- E = 9.6 +/- 0.490 = 9.110 10.090

CI = 9.11 , 10.09

(c) We are 95% confident that the true population mean lies between 9.11 to 10.09.

(d)

Ho: = 11

Ha: 11

z = - 5.6918

Critical Value of Z (Two Tailed): ± 1.96

As z stat falls in the rejection area, we reject the Null hypothesis.

As as 11 is not in the CI range ( 9.11 to 10.09), we reject the Null hypothesis.  

Hence we have sufficient evidence to believe that the average diameter of the flowers of
a particular plant is not equal to 11.