Consider the hypothesis statement to the right using = 0.01 and the data to the
ID: 3351536 • Letter: C
Question
Consider the hypothesis statement to the right using = 0.01 and the data to the right from Ho -u2 so two independent samples. a) Calculate the appropriate test statistic and interpret the result b) Calculate the p-value and interpret the result Click here to view page 1 of the standard nomal table. Click here to view page 2 of the standard normal table. x1 = 83 o, 27 -55 X2=75 ng-60 a) The test statistic is (Round to two decimal places as needed.) Enter your answer in the answer box and then click Check Answ 4 remaining parts AllExplanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: 1 - 2< 0
Alternative hypothesis: 1 - 2 > 0
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the mean difference between sample means is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.01. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees offreedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 4.3191
DF = 113
t = [ (x1 - x2) - d ] / SE
t = 1.85
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is thesize of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.
The observed difference in sample means produced a t statistic of 1.85. We use the t Distribution Calculator to find P(t > 1.85).
Therefore, the P-value in this analysis is 0.0335.
Interpret results. Since the P-value (0.0335) is greater than the significance level (0.01), we cannot reject the null hypothesis.