e Taken:1:18:34 Yahaira Amaro: Attempt 1 Question 10 (3.5 points) Assu me that t
ID: 3314035 • Letter: E
Question
e Taken:1:18:34 Yahaira Amaro: Attempt 1 Question 10 (3.5 points) Assu me that the assumptions and conditions for inference with a two-sample t-test are met. Test the indicated claim about the means of the two populations. State your conclusion A new type of flare accelerant is tested A control group of flares (x) that are currently used and a group of flares (Y) with the new accelerant are tested for their burning times (in minutes) and sample results are given below Flare X Flare Y n=35 n = 40 x = 19.4 15.1 s=1.4 s = 0.8 Refer to the sample data to test the claim that the two populations have equal means. Use a 005 significance level Test statistic t = 16.025. P-value ~ 0Explanation / 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 two-tailed test. The null hypothesis will be rejected if the difference between sample means is too big or if it is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. 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 of freedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 0.2683
DF = 73
t = [ (x1 - x2) - d ] / SE
t = 16.025
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size 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 the population means, and SE is the standard error.
Since we have a two-tailed test, the P-value is the probability that a t statistic having 73 degrees of freedom is more extreme than -16.025; that is, less than -16.025 or greater than 16.025.
Thus, the P-value = 0.
Interpret results. Since the P-value (almost 0) is less than the significance level (0.05), we cannot accept the null hypothesis.
Reject H0, We can conclude that there is significant difference between means of two population.
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