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Hypothesis tests lead to a ___ regarding the null hypothesis, while confidence intervals provide a___ for the parameter. range; decision rejection; estimate estimate; rejection

Ask by Davison Todd. in the United States
Mar 10,2025

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Hypothesis tests lead to a decision regarding the null hypothesis, while confidence intervals provide an estimate for the parameter.

Solution

To fill in the blanks correctly, let's analyze the statements: 1. **Hypothesis tests lead to a ___ regarding the null hypothesis**: In hypothesis testing, we either reject or fail to reject the null hypothesis based on the evidence from the data. Therefore, the appropriate word here is "decision." 2. **Confidence intervals provide a ___ for the parameter**: Confidence intervals are used to estimate the range of values for a population parameter based on sample data. Thus, the correct word here is "estimate." Putting it all together, the correct completion of the statement is: **Hypothesis tests lead to a decision regarding the null hypothesis, while confidence intervals provide an estimate for the parameter.** So the answer is: **range; decision**.

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Hypothesis tests lead to a **rejection** regarding the null hypothesis, while confidence intervals provide an **estimate** for the parameter. Essentially, when conducting a hypothesis test, you are looking to determine whether there is enough evidence to reject the null hypothesis in favor of an alternative. On the other hand, confidence intervals help us capture the likely range of values for a population parameter, giving us a more nuanced view of uncertainty in our estimates. To make hypothesis testing and confidence intervals effective tools in your statistical toolbox, it’s crucial to select appropriate significance levels and sample sizes ahead of time. A common mistake is neglecting assumptions, such as normality in your data, which can lead to misleading results. Always double-check your assumptions to ensure your tests and intervals hold up under scrutiny!

Related Questions

Question 12(Mulliple Choice Warth 5 points) \[ (04.06 \mathrm{HC}) \] A researcher wants to test the claim that the proportion of juniors who watch television regularly is greater than the proportion of seniors who watch television regularly She finds that 56 of 70 randomly selected juniors and 47 of 85 randomly selected seniors report watching television regularly. Construct \( 95 \% \) confidence intervals for each population proportion. Which of the statemente gives the correct outcome of the research or's tert of the dalim? The \( 95 \% \) confidence interval for juniors is (706, 894), and the \( 95 \% \) confidence interval for seniors is ( 447,659 ). Since the intervals overlap, there is not enough evidence to say the proportion of juniors who watch television regularly may be higher than that of seniors. The \( 95 \% \) confidence interval for juniors is (721, 879), and the \( 95 \% \) confidence interval for seniors is (464, 642). Since the interval for juniors is higher than the interval for seniors, there is evidence to say the proportion of juniors who watch television regularly may be higher than that of seniors. The \( 95 \% \) confidence interval for juniors is ( 706,894 ), and the \( 95 \% \) confidence interval for seniors is ( 447,659 ). Since the interval for juniors is higher than the interval for seniors, there is evidence to say the proportion of juniors who watch television regularly may be higher than that of seniors. The \( 95 \% \) confidence interval for juniors is ( \( 721, .879 \) ), and the \( 95 \% \) confidence interval for seniors is (464, 642). Since the intervals overlap, there is not enough evidence to say the proportion of juniors who watch television regularly may be higher than that of seniors.

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