Question

Consider the following hypothesis test: Ho: u=15 Ha: u15 A sample of 40 provided a sample mean of 14.16. The population standard deviation is 6. Enter negative value as negative number. a. Compute the value of the test statistic (to 2 decimals) b. What is the p-value (to 4 decimals)? Use the value of the test statistic rounded to 2 decimal places in your calculations. c. Using a 0.05, can it be concluded that the population mean is not equal to 15? - Select your answer- Answer the next three questions using the critical value approach. d. Using a 0.05, what are the critical values for the test statistic? ( or -) (to 2 decimals) State the rejection rule: Reject Ho if z is-Select your answer the lower critical value and is -select your answer the upper critical value. Can it be concluded that the population mean is not equal to 15? - Select your answer

3-7

Answer 1

a. Here population standard deviation is known so we will use z statistics to find test statistics

$z=\frac{\overline{x}-\mu}{\frac{\sigma }{\sqrt{n}}}=\frac{14.16-15}{\frac{6}{\sqrt{40}}}=-0.89$

b. P value is $2*P(z<-0.89)=2*0.1867=0.3734$

c. As P value is greater than $\alpha=0.05$, we fail to reject the null hypothesis

Hence we conclude that mean is equal to 15.

d. The z-critical values for a two-tailed test, for a significance level of α=0.05

zc​=−1.96 and zc​=1.96

Graphically

Critical Values Normal Distribution 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 -4.0 -3.5 -3.0-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Reject H0 if z is less than the lower critical value and is greater than the upper critical value.

As z statistics is not falling in the rejection region, we fail to reject the null hypothesis

Hence we conclude that mean is equal to 15.