2 You wish to test the following claim (He) at a significance level of = 0.10. Y

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2

You wish to test the following claim (He) at a significance level of = 0.10. You believe both populations are normally distributed, but you do not know the standard deviations for cither. And you have no reason to believe the variances of the two populations are equal. You obtain a samaple of size n standard deviation ofs1 5.6 rom the irst po n ation You o tatn a sample of size n2 12 with mean of2 63 and a standard deviation of 14.6 rom the second population -14 with a mcan of 66.6 and a a. What is the test statistie foa this sanuple? test statastic- Raund to 4 decimal places. b. What is the p-value for this sample? p-value = Round to 4 decimal places. c. The p-value is.. less than (or equal to) a greater than d. This test statistic leads to a decision to... reject the null accept the ull fail to relect the null e. As such, the final conlusi is tha. There is sufficient evidence to warrant rejection of the claim that the first population mean is greater than the second population mean. There is not sufficien evideneto warrant rejection ofthe clathat the first papulation mean is greater than the second population mean The sample data support the claim that the first population mcan is greatcr than the second population mcan. 0 i e s tiot sul sample ew ene lo su potl Ibe elain thale ust popul tot lti azi is lealet lhari lhe second popula um mean. Get help Video

Explanation / Answer

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: 1< 2
Alternative hypothesis: 1 > 2

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 0.10. 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 = 4.473

DF = 24

t = [ (x1 - x2) - d ] / SE

t = 0.805

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.

Therefore, the P-value in this analysis is 0.209.

Interpret results. Since the P-value (0.209) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Fail to reject the null hypothesis.

There is sufficient evidence to warrant rejection of the claim that the first population mean is greater than the second population mean.

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