Question

You may need to use the appropriate technology to answer this question. Consider the following hypothesis test. Holly - 12 = 0 Ha: My - 4270 The following results are from independent samples taken from two populations. Sample 1 Sample 2 ni = 35 n2 = 40 * = 13.6 X2 = 10.1 $i = 5.4 $2 = 8.8 (a) What is the value of the test statistic? (Use xa - 2. Round your answer to three decimal places.) (b) What is the degrees of freedom for the t distribution? (Round your answer down to the nearest integer.) (c) What is the p-value? (Round your answer to four decimal places.) p-value = (d) At a = 0.05, what is your conclusion? O Do not Reject H,. There is insufficient evidence to conclude that ủy – Hy +0. Reject Ho. There is insufficient evidence to conclude that – # 0. Reject Ho. There is sufficient evidence to conclude that u1 – M2 + 0. Do not Reject Ho. There is sufficient evidence to conclude that ', - 4270.

Answer 1

a)

The test statistic is given by:

11-12 13.6 – 10.1 t 2.103 5.42 V 35 + 8.82 40 + n2

b)

Required degrees of freedom = $n_1+n_2-2=35+40-2=73$

c)

Since this is a two-tailed test, so the p-value is given by:

$\\2\times P(t_{73}>2.103)=2\times 0.019457=0.038914\approx 0.0389$

d)

Since p-value is less than 0.05, so we have sufficient evidence to reject the null hypothesis H0.

Reject H0. There is sufficient evidence to conclude that $\mu_1\neq \mu_2$ .

Hence 3rd option.