Please provide the following information for Problems 15-26 and 29-35 (a) What i

Question

Please provide the following information for Problems 15-26 and 29-35 (a) What is the level of significance? State the null and alternate hypotheses (b) Check Requirements What sampling distribution will you use? What (c) Find (or estimate) the P-value. Sketch the sampling distribution and show the null hypothesis? Are the data statistically significant at level ? assumptions are you making? Compute the sample test statistic and cor responding z or t value as appropriate. the area corresponding to the P-value. (d) Based on your answers in parts (a) to (c), will you reject or fail to reject

Explanation / Answer

Solution:-

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

Null hypothesis: Experimental< Control
Alternative hypothesis: Experimental > Control

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 of freedom (DF), and the t statistic test statistic (t).

SE = sqrt[(s12/n1) + (s22/n2)]
SE = 12.60
DF = 58

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

t = 1.52

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 population means, and SE is the standard error.

The observed difference in sample means produced a t statistic of 1.52. We use the t Distribution Calculator to find P(t > 1.52).

Therefore, the P-value in this analysis is 0.067.

Interpret results. Since the P-value (0.067) is greater than the significance level (0.01), we cannot reject the null hypothesis.

From the above test we do not have sufficient evidence in the favor of the claim that the experimental group performed better than the control group.

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