If a sample provides a 95% confidence interval ranging from 160 to 240 for a mean estimate, how would a hypothetical population mean of 250 be evaluated?

Suppose a research study finds that a sample of students provides a mean calorie estimate for a cookie of 200, with a 95% confidence interval ranging from 160 to 240. Match each numerical value or range to its correct interpretation in this statistical example.

In a study testing a new mnemonic device, the 95% confidence interval for the mean number of items recalled is [15.5, 19.5]. If the hypothesized population mean is 12.0, this value is considered statistically significantly different from the sample mean at the .05 alpha level.

A researcher studying calorie estimation finds a sample mean of 200 with a 95% confidence interval of [160, 240]. Arrange the logical steps in order to analyze why a hypothesized population mean of 250 would be considered statistically significantly different from this sample mean.

A researcher is designing the results section for a study on the average reaction time (in milliseconds) of participants during a cognitive task. The sample mean is $450$ ms. To create a report where a hypothesized population mean of $500$ ms is considered statistically significantly different from the sample mean at the $.05$ alpha level, which of the following boundary configurations must the researcher report for their $95\%$ confidence interval ($CI$)?

In the provided example, a hypothetical population mean that falls within the range of the $95\%$ confidence interval ($160$ to $240$) is considered statistically significantly different from the sample mean at the $.05$ alpha level.

Based on the example of calorie estimates for a cookie, arrange the following steps of the statistical process in the correct logical order, starting from the specific sample result and ending with the broader population inference.

A study on university students finds a mean calorie estimate for a cookie of $200$, with a $95\%$ confidence interval ranging from $160$ to $240$. When evaluating a hypothesis that predicts the true population mean is $250$, a researcher would conclude that the difference between this hypothesized value and the sample mean is statistically _____ at the $.05$ alpha level.

A researcher studying weekly exercise duration in college students finds a sample mean of $150$ minutes per week, with a $95\%$ confidence interval of [$120$, $180$] minutes. Match each hypothetical population mean to the correct conclusion about statistical significance at $α = .05$.

A researcher studying nightly sleep duration in college students finds a $95\%$ confidence interval of [$6.2$, $7.8$] hours. The researcher concludes: 'Because $7.0$ hours falls inside the confidence interval, it is statistically significantly different from the sample mean at $α = .05$.' A student carefully evaluating this conclusion correctly judges it to be _____, because values inside a $95\%$ confidence interval are NOT considered statistically significantly different from the sample mean.

Based on the course example, recall and describe the key components of the cookie calorie estimation study. In your response, state the sample size, the sample mean, the $95\%$ confidence interval range, and how a hypothetical population mean of $250$ is evaluated in comparison to the sample mean at the $.05$ alpha level.

Explain what this interval indicates about the true mean calorie estimate for the population of university students, and justify whether a hypothesized population mean of $250$ is statistically significantly different from the sample mean.

If a researcher obtains a sample mean of $200$ calories and a $95\%$ confidence interval of $160$ to $240$ for a cookie calorie estimation task, apply this information to evaluate the claim that the true population mean is $250$. State whether this claim is statistically significantly different at the $.05$ alpha level and explain why.