Question

e that you have ฮ sa pic c n, 5, with the sampe moan 45, and ฮ ” le standard de s on o s 1-4 and you have a ndependent sampe o n2-5 tom another population with a sample moan o X2-35 and he samplc sarda d deviation S2-3. Assuming he populaton vanances are equal the 0.01 Find the tost statistc. STAT Round to two decimsl places as needed.) Find the pvaue. p-vaRound to three decimal placesanooded.) Ο A. Ο B. O C. O D. Reject H0. There is sufficient evidence that μ1 > μ2. Do not re ect Ho. There is insufficient evidence that μι > μ2. Do not reject Ho. There is sifiaert endence that μ1 > μ2. Reject Ho-Theres rsuticent evidence th 1 > μ2.

Answer 1

Hypothesis : $H_0:\mu_1\leq \mu_2$ Vs $H_1:\mu_1> \mu_2$

The pooled estimate is ,

$S=\sqrt{\frac{(n_1-1)s^2+(n_2-1)s_2^2}{n_1+n_2-2}}=\sqrt{\frac{(5-1)4^2+(5-1)3^2}{5+5-2}}=3.5355$

The test statistic is ,

$t=\frac{\bar{X_1}-\bar{X_2}}{S\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}\to t_{n_1+n_2-2}$

$=\frac{45-35}{3.5355\sqrt{\frac{1}{5}+\frac{1}{5}}}=4.47$

P-value = $P(t_[d.f.]>|t_{stat}|)=P(t_{5+5-2}>4.47)=0.001$ ; From excel "=TDIST(4.47,8,1)"

Decision : Here , P-value = 0.001 < $\alpha=0.01$

Therefore , reject Ho

Conclusion : Reject Ho . There is sufficient evidence that $\mu_1> \mu_2$