A paint company produces glow in the dark paint with an advertised glow time of 15 min. A painter is interested in finding out if the product behaves worse than advertised. She sets up her hypothesis statements as H0 : µ ≤ 15 and Ha : µ > 15, then calculates a test statistic of z = −2.30. What would be the conclusions of her hypothesis test at significance levels of α = 0.05, α = 0.01, and α = 0.001?

Now we can decide based on the significance level . If we reject the null hypothesis and in other case we FAIL to reject the null hypothesis.

we see that so then we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly less than 15

we see that so then we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is NOT significantly less than 15

we see that so then we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is NOT significantly less than 15

Explanation:

For this case they conduct the following system of hypothesis for the ture mean of interest:

Null hypothesis:

Alternative hypothesis:

The statistic for this hypothesis is:

And on this case the value is given

For this case in order to take a decision based on the significance level we need to calculate the p value first.

Since we have a lower tailed test the p value would be:

Now we can decide based on the significance level . If we reject the null hypothesis and in other case we FAIL to reject the null hypothesis.

we see that so then we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly less than 15

we see that so then we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is NOT significantly less than 15

we see that so then we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is NOT significantly less than 15