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A random survey of 75 death row inmates revealed that the mean length of time on death row is 17.4 years with a standard deviation of 6.3 years. Conduct a hypothesis test to determine if the population mean time on death row could likely be 15 years. Is this a test of one mean or proportion? State the null and alternative hypotheses. H_o: H_a: Is this a right-tailed, left-tailed, or two-tailed test? What symbol represents the random variable for this test? In words, define the random variable for this test. Is the population standard deviation known and, if so. what is it? Calculate the following: Which test should be used? State the distribution to use for the hypothesis test. Find the p -value. Al a pre -conceived a = 0.05, what is your Decision: Reason for the decision: Conclusion (write out in a complete sentence):

Respuesta :

  • The test is the test for a mean.
  • The null hypothesis is of: [tex]H_0: \mu = 15[/tex]
  • The alternative hypothesis is of: [tex]H_1: \mu \neq 15[/tex]
  • The test is two-tailed.
  • The symbol that represents the random variable for this test is of: [tex]\mu[/tex]
  • The variable represents the mean time spent on the death row by the prisoners.
  • The population standard deviation is not known.
  • The test should be used is a two-tailed t-test.
  • The distribution used is the t-distribution.
  • The p-value for the test is of: 0.0015.
  • The decision is of: Reject the null hypothesis.
  • The conclusion is of: There is enough evidence that prisoners spend a time different of 15 years in the death row.

What are the hypothesis test?

At the null hypothesis, it is tested if the mean is of 15 years, that is:

[tex]H_0: \mu = 15[/tex]

At the alternative hypothesis, it is tested if the mean is different of 15 years, that is:

[tex]H_1: \mu \neq 15[/tex]

What is the test statistic?

The equation that gives the test statistic is defined as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which:

  • [tex]\overline{x}[/tex] is the sample mean.
  • [tex]\mu[/tex] is the value tested at the null hypothesis.
  • s is the standard deviation of the sample.
  • n is the sample size.

The values of these parameters in this problem are given as follows:

[tex]\overline{x} = 17.4, \mu = 15, s = 6.3, n = 75[/tex]

Hence the test statistic is of:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{17.4 - 15}{\frac{6.3}{\sqrt{75}}}[/tex]

t = 3.30.

What is the p-value?

Considering a two-tailed test, as we are testing if the mean is different of a value, with t = 3.30 and 75 - 1 = 74 df, the p-value of the test is of:

0.0015.

Since the p-value is less than the significance level of 0.05, the null hypothesis is rejected, meaning that there is enough evidence to conclude that prisoners spend a time different of 15 years in the death row.

More can be learned about the test of an hypothesis at https://brainly.com/question/13873630

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