Question

Test the claim about the difference between two population means phy and ly at the level of significance a. Assume the samples are random and independent, and the populations are normally distributed Claim: My SM2; &#0.01. Assume o to Sample statistics: X2 = 2413, 5, - 176, n, = 14 and X2 - 2306, 6, 53, n2 - 11 Identify the null and alternative hypotheses. Choose the correct answer below. O A HO:44 <H2 Hg: 49 212 Oc. Họ t = 92 Haikal O E. Ho: P2 Ho: R15h Find the standardized test statistic t. OB. Ho512 Ho:1412 OD. H: 212 HH2 OF Hy: 12 H:12 (Round to two decimal places as needed.) Find the P-value P. (Round to three decimal places as needed.)

Answer 1

given that

$n_1=14,n_2=11,\bar{x}_1=2413,\bar{x}_2=2306,s_1=176,s_2=53$

we have to test that if there is difference in two means or not hence

$H_0: \mu_1 =\mu_2 ,H_a: \mu_1 \neq \mu_2$

option (C) is correct

since we have assumed that two population variances are unequal hence test statistics is given by

1-1 2413-2306 107 t= 49.68 + 17be 14 + 32 11 發 LT 212

=2.15

DF= Min{(n1-1),(n2-1)} =min{(14-1),(11-1)}=Min{13,10} =10

since test is two tailed so

P-Value =2*P(Z>2.15)=2*0.0285=0.057

since P value is more than level of significance Hence we failed to reject H0 hence there is no enough evidence to support the claim that there is difference in the two means.