Question

For a sample of 35 items from a population for which the standard deviation is 20.5, the sample mean is 458. At the 0.05 level of significance, test H0: µ = 450 verses H1: µ ≠ 450. What is the calculated value of test statistic? (Specify your answer to the 2nd decimal.)

Answer 1

Answer:

Value of test statistics = 2.30

Step-by-step explanation:

We are given that for a sample of 35 items from a population for which the standard deviation is 20.5, the sample mean is 458.

Also, Null Hypothesis, $H_0$ : $\mu$ = 450

Alternate Hypothesis, $H_1$ : $\mu\neq$ 450

The test statistics that will be used here is One sample t-test statistics;

              T.S. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean = 458

             s = sample standard deviation = 20.5

            n = sample of items = 35

So, test statistics = $\frac{458-450}{\frac{20.5}{\sqrt{35} } }$ ~ $t_3_4$

                            = 2.30

Therefore, the value of test statistics is 2.30 .