Question

Math

Posted 3 months ago

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True or False: A sample is used to obtain a 95% confidence interval for the mean of a population. The confidence interval goes from 15 to 19.
If the same sample had been used to test the null hypothesis that the mean of the population is equal to 20 versus the alternative hypothesis that the mean of the population differs from 20, the null hypothesis could be rejected at a level of significance of 0.10. True or false?
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Answer from Sia

Posted 3 months ago

Solution by Steps

step 1

To determine if the null hypothesis that the population mean is equal to 20 can be rejected, we need to consider the confidence interval and the level of significance

step 2

The given 95% confidence interval for the population mean is from 15 to 19. This interval does not include the hypothesized population mean of 20

step 3

If the hypothesized mean (20) lies outside the 95% confidence interval, it would also lie outside the confidence interval corresponding to a higher level of significance (0.10), which is less stringent than 0.05

step 4

Since the level of significance of 0.10 corresponds to a 90% confidence interval, which is wider than the 95% confidence interval, the null hypothesis would be rejected at the 0.10 level of significance

Answer

True

Key Concept

Confidence Interval and Hypothesis Testing

Explanation

If a hypothesized mean lies outside a 95% confidence interval, it will also lie outside a 90% confidence interval, leading to rejection of the null hypothesis at a 0.10 level of significance.

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