Statistic Question hekp?

Question

Height of trees at a christmas tree lot follow a normal distribution with standard deviation 34 cm. A random sample of 18 trees was selected and it was found that they had a mean height of 227 cm.

a) conduct a hypothesis test at the 10% level of significance to determine whether the true mean height of all christmas trees on the lot differs from 215 cm. show all of your steps, including hypotheses, the calculation of the test statistics and the p-value, and properly worded conclusion.

Answer 1

Since we know the distribution of heights is normal with known standard deviation we can use the z-statistic to test the true mean.

Ho: true mean = 215

Ha: true mean != 215

z-statistic = (xbar - true mean)/(std dev/sqrt(sample size)

z = (227-215) / 34/sqrt(18) = 2.75

p-value = P(z > 2,75) + P(z < -2.75)

since normal distribution is symmetric that is the same as 2*P(z <-2.75) = 2*0.0030 = 0.006

since the p-value < 0.1, we will reject the null hypothesis and state that there is conclusive evidence that the true mean of xmas tree heights differs from 215.