Math

StatisticsQ&A Library18. a. A repeated-measures study with a sample of n = 16 participants produces a mean difference of MD = 4 with a standard deviation of s = 8. Use a two-tailed hypothesis test with α = .05 to determine whether it is likely that this sample came from a population with µD = 0.b. Now assume that the sample mean difference is MD = 10, and once again visualize the sample distribution. Use a two-tailed hypothesis test with α = .05 to determine whether it is likely that this sample came from a population with µD = 0.c. Explain how the size of the sample mean difference influences the likelihoodQuestion

Asked Jan 16, 2020

6 views

18. a. A repeated-measures study with a sample of n = 16 participants produces a mean difference of MD = 4 with a standard deviation of s = 8. Use a two-tailed hypothesis test with α = .05 to determine whether it is likely that this sample came from a population with µD = 0.

b. Now assume that the sample mean difference is MD = 10, and once again visualize the sample distribution. Use a two-tailed hypothesis test with α = .05 to determine whether it is likely that this sample came from a population with µD = 0.

c. Explain how the size of the sample mean difference influences the likelihood

Step 1

**a)**

Null hypothesis:

*µ _{D}=*0

Alternative hypothesis:

*µ _{D}≠*0

This is a two tailed test.

Since the population standard deviation is unknown, the appropriate test is one sample *t*-test.

The test statistic value can be obtained as follows:

Step 2

*Computation of P-value:*

The *P*-value for the two tailed *t*-value at 15 degrees of freedom is **0.0639** which can be can be obtained using the excel formula** “=T.DIST.2T (2, 14)**”.

Assume that the level of significance is 0.05.

**Decision rule:**

If p-value ≤α, then reject the null hypothesis. Otherwise, do not reject the null hypothesis.

**Conclusion:**

Here, p-value (0.0639) is greater than the level of significance (0.05).

Therefore, fail reject the null hypothesis.

**There is sufficient evidence to conclude that the sample is came from a population with ***µD=***0****.**

...

Tagged in

Find answers to questions asked by student like you

Show more Q&A

Q: True? When we collect random samples to test the claim that the proportion of female CIA agents stat...

A: In a binomial distribution with total number of trails n and probability of success p, the normal ap...

Q: Regarding multiple linear regression analysis: a. What sum of squares is made as small as possible ...

A: a. The sum of squares of residuals (error) should be made as small as possible when finding the best...

Q: suppose x1 and x2 are predictor variables for a response variable y. a. The distribution of all poss...

A: It is provided that x1 and x2 are predictor variables for a response variable y.a. Yes, the distribu...

Q: Smoking Stopped In a program designed to help patients stop smoking, 198 patients were given sustain...

A: According to the provided data, in a stop smoking program, 198, n patients were given sustained care...

Q: Smoking Stopped In a program designed to help patients stop smoking, 198 patients were given sustain...

A: For sustained care:The sample proportion is 0.828.The sample size is 198.Consider the confidence int...

Q: Basis for the Range Rule of Thumb and the Empirical Rule. In Exercise, find the indicated area under...

A: The required area under the z score -3 and 3 can be obtained as:

Q: Birth Weights Based on Data Set 4 “Births” in Appendix B, newborn males have weights with a mean of ...

A: z score for the male:Let X be the weight for newborn males.The formula for the z score is,

Q: Sorting Hat At Hogwarts School of Witchcraft and Wizardry, the Sorting Hat chooses one of four house...

A: Here, n = 16, r = 4.The first-year students are selected is not of importance here. What matters is ...

Q: Detecting Fraud The Brooklyn District Attorney’s office analyzed the leading (leftmost) digits of ch...

A: a)Define the random variable x as the number of checks with the leading digit as 1. Here, the number...