Question

Minimum Wage

	Name of state	Data value
State 1	Alabama	2.2
State 2	Arkansas	0.7
State 3	Connecticut	0.9
State 4	Florida	6.6
State 5	Idaho	0.6
State 6	Iowa	1.2
State 7	Louisiana	2.9
State 8	Massachusetts	1.9
State 9	Mississippi	1.3
State 10	Nebraska	0.5
State 11	New Jersey	2.2
State 12	North Carolina	4.6
State 13	Oklahoma	1.4
State 14	Rhode Island	0.4
State 15	Tennessee	3.4

Analysis:

Compute the mean and standard deviation of the sample data:

Mean =

Standard deviation =

Sample size =

Hypothesis test(claim):

Based on the claim you made above, conduct a hypothesis test.

Level of significance (choose from 5% or 1%): which did you pick?

Null hypothesis - H0: µ

Alternative hypothesis - Ha: µ

In words, clearly state what your random variable X represents:

Which distribution you will use for the test, Normal or Student’s t (if t-distribution, state the degrees of freedom):

What is the test statistic?

What type of test is used: two-tailed, right-tailed, left-tailed?

What is the p-value?
In one or two complete sentences, explain what the p-value means for this test:

Use the above information to sketch a picture of this situation on the graph below. Clearly label and scale the horizontal axis and shade the region(s) corresponding to the p-value.

Decision and Conclusion: Indicate the correct decision (“reject” or “do not reject” the null hypothesis), the reason for it, and write an appropriate conclusion about your claim using complete sentences.

• Alpha:

• Decision:

• Reason for decision:

• Conclusion:

Construct a 95% confidence interval for the true mean. Include a sketch of the graph of the situation on the distribution below. Label the point estimate and the lower and upper bounds of the confidence interval.

Answer 1

Compute the mean and standard deviation of the sample data:

Mean = 2.0533

Standard deviation = 1.7299

Sample size = 15

Hypothesis test: µ = 2

Based on the claim you made above, conduct a hypothesis test.

Level of significance (choose from 5% or 1%): which percent did you use? 0.05

Null hypothesis - H0: µ = 2

Alternative hypothesis - Ha: µ $\neq$ 2

In words, clearly state what your random variable X represents: X represents the data value.

Which distribution you will use for the test, Normal or Student’s t (if t-distribution, state the degrees of freedom): Student's t df = 14

What is the test statistic? 0.119

What type of test is used: two-tailed, right-tailed, left-tailed? two-tailed

What is the p-value? 0.9067
In one or two complete sentences, explain what the p-value means for this test: The probability that the results are equal to or greater than µ = 2 is 0.9067.

Use the above information to sketch a picture of this situation on the graph below. Clearly label and scale the horizontal axis and shade the region(s) corresponding to the p-value.

Distribution Plot T, df=14 0.4 0.3 Density 0.2 0.1 0.4533 0.4533 0.0 -0.019393 X

Decision and Conclusion: Indicate the correct decision (“reject” or “do not reject” the null hypothesis), the reason for it, and write an appropriate conclusion about your claim using complete sentences.

• Alpha: 0.05

• Decision: Fail to reject the null

• Reason for decision: Since the p-value (0.9067) is greater than the significance level (0.05), we fail to reject the null hypothesis.

• Conclusion: Therefore, we can conclude that µ = 2.

Construct a 95% confidence interval for the true mean. Include a sketch of the graph of the situation on the distribution below. Label the point estimate and the lower and upper bounds of the confidence interval.

The 95% confidence interval for the true mean is between 1.0953 and 3.0113.