Question

A horticulturist wishes to estimate the true mean growth of seedlings in a large timber plot last year. A random sample of 20 seedlings is selected and the one-year growth for each of them is measured. The sampled seedlings have a mean growth of 6.4 cm and a standard deviation of 1.5 cm. One-year seedling growth is known to follow a normal distribution with standard deviation 2.0 cm. We wish to conduct a hypothesis test at the 10% level of significance to determine whether the true mean one-year seedling growth differs from 6.0 cm. The rejection region for the test is:

(A) |z| > 1.645 (B) t > 1.328 (C) z > 1.282 (D) |t| > 1.729 (E) |z| > 1.282

Please show all steps for the answer

Answer 1

here since standard deviation of the distribution is known , therefore we should use z distribution

also we are checking if mean differs from 6.0 cm (irrespective of direction weather less or high) , therefore it is 2 tailed test,

Now for 2 tailed test and 0.10 level crtiical value of z= 1.645 (from invnorm(0.95,0,1) function of ti-84)

option A is correct

(A) |z| > 1.645