A study was done using a treatment group and a placebo group. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.100.10 significance level for both parts. TreatmentPlacebo μμ1μ2n2732(overbar) x 2.352.65s0.920.57 Test the claim that the two samples are from populations with the same mean.What are the null and alternative hypotheses? The test statistic, t, is _______ The P-value is _______ State the conclusion for the test? Construct a confidence interval suitable for testing the claim that the two samples are from populations with the same mean______ <μ1 − μ2 < ______

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A study was done using a treatment group and a placebo group. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.100.10 significance level for both parts.

	Treatment	Placebo
μ	μ1	μ2
n	27	32
(overbar) x	2.35	2.65
s	0.92	0.57

Test the claim that the two samples are from populations with the same mean.

What are the null and alternative hypotheses?

The test statistic, t, is _______

The P-value is _______

State the conclusion for the test?

Construct a confidence interval suitable for testing the claim that the two samples are from populations with the same mean
______ <μ1 − μ2 < ______

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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