For a hypothesis test of H0 : μ = 8 vs. H0 : μ > 8, the sample mean of the data is computed to be 8.24. The population standard deviation is unknown; the sample standard deviation is computed, and its value is 0.29. These sample statistics are based on a sample size of 19. It is assumed that the underlying population is normally distributed. Which of the following would be the distribution of the test statistic in this scenario? a) The t-distribution with 8 degrees of freedomb) The standard normal distributionc) The t-distribution with 19 degrees of freedomd) The t-distribution with 18 degrees of freedom

Question

Jett

Mathematics

1 July, 07:11

For a hypothesis test of H0 : μ = 8 vs. H0 : μ > 8, the sample mean of the data is computed to be 8.24. The population standard deviation is unknown; the sample standard deviation is computed, and its value is 0.29. These sample statistics are based on a sample size of 19. It is assumed that the underlying population is normally distributed. Which of the following would be the distribution of the test statistic in this scenario? a) The t-distribution with 8 degrees of freedomb) The standard normal distributionc) The t-distribution with 19 degrees of freedomd) The t-distribution with 18 degrees of freedom

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Answers (1)

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Rodrigo · Answer 1

d) The t-distribution with 18 degrees of freedom

Step-by-step explanation:

If we have the population standard deviation, we use the standard normal distribution.

Otherwise, if we only have the standard deviation for the sample, we use the t-distribution.

The number of degrees of freedom is the sample size subtracted by 1.

In this problem:

Sample size of 19, we have the standard deviation for the sample.

So the t-distribution will be used to solve this question, with 19-1 = 18 degrees of freedom.

So the correct answer is:

d) The t-distribution with 18 degrees of freedom