Question

Explain how you found the test statistic and p-value?

Assume that a simple random sample has been solocted from a normally distributed population. Find the test statistic and P-value. Points: 5 19) Test the claim that the mean lifetime of car engines of a particular type is greater than 220,000 miles. Sample data are summarized as n = 23, X = 226,450 miles, and s = 11,500 miles. Use a significance level of a = 0.01. test statistic (1.5 points) P-value (1.5 points) Explain how you found the test statistic and p-value. (2 points)

Answer 1

Now , the null and alternatiev hypothesis is ,

$H_0:\mu=220000$

$H_1:\mu>220000$

The test is right-tailed test.

Now , df=degrees of freedom=n-1=23-1=22

The test statistic is,

$t_{stat}=\frac{\bar{X}-\mu_0}{s/\sqrt{n}}=\frac{226450-220000}{11500/\sqrt{23}}=2.690$

The p-value is ,

p-value=$P(t_{df}>|t_{stat}|)=P(t_{22}>2.690)=0.0067$ ; The Excel function is , =TDIST(2.690,22,1)