Question

You wish to test the following claim H₁ at a significance level of α = 0.005. H₀: μ = 76.5, H₁: μ ≠ 76.5. You believe the...........

Answer 1

The question is about conducting a hypothesis test for a population mean with a significance level of 0.005. The provided information suggests setting up a two-tailed test to determine if there is sufficient evidence to reject the null hypothesis that the population mean is 76.5 in favor of the alternative hypothesis that the population mean is not equal to 76.5.

Step-by-step explanation:

The student is asking about hypothesis testing in statistics, which involves comparing a sample statistic to a population parameter to determine if there is enough evidence to support a specific claim about the population parameter. The claim being tested here is that the population mean (μ) is not equal to 76.5. Given a significance level (α) of 0.005, we would set up a two-tailed test because the alternative hypothesis H1 indicates that the population mean could be either greater than or less than 76.5.

In hypothesis testing, the null hypothesis H0: μ = 76.5 represents the status quo, while the alternative hypothesis H1: μ ≠ 76.5 suggests there is a difference from this established value and we will need evidence to support rejecting H0. The significance level of 0.005 is quite low, indicating that we would require strong evidence against the null hypothesis before rejecting it in favor of the alternative.

The test statistic would be calculated using sample data, and then we would compare it to critical values from an appropriate distribution (normally the standard normal distribution if the sample size is large or the population standard deviation is known, or the t-distribution if the population standard deviation is unknown and the sample size is small) to determine whether to reject or not reject the null hypothesis. The decision would be based on whether the calculated test statistic falls into the rejection region determined by the significance level.

Answer 2

Conduct a two-tailed hypothesis test using a critical value approach or a p-value approach, comparing the test statistic to the critical value or p-value at the 0.005 significance level.

Step-by-step explanation:

To test the claim H₁: μ ≠ 76.5 at a significance level of α = 0.005, you would use either a critical value approach or a p-value approach. In the critical value approach, you compare the test statistic to the critical values from the standard normal distribution corresponding to the chosen significance level. In the p-value approach, you calculate the probability of obtaining a test statistic as extreme as the one observed, assuming the null hypothesis is true, and compare it to the significance level.

If the test statistic falls beyond the critical values or the p-value is less than α, you reject the null hypothesis, providing evidence in favor of H₁: μ ≠ 76.5.

Understanding hypothesis testing procedures and significance levels is essential in statistics, enabling researchers to make informed decisions based on collected data.