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Example of a Confidence Interval
To illustrate a confidence interval, suppose a sample of university students provides a mean calorie estimate for a cookie of , with a confidence interval ranging from to . Under the interval procedure's assumptions, refers to its long-run coverage: if samples were repeatedly drawn from the same population and intervals constructed in the same way, approximately of those intervals would contain the true population mean. It does not assign a probability to the fixed mean lying between and in this realized interval (NIST’s explanation of confidence intervals). Furthermore, this interval allows for hypothesis testing; any hypothetical population mean outside of this to range (such as a hypothetical value of ) would be considered statistically significantly different from the sample mean at the .05 alpha level.
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Research Methods in Psychology - 4th American Edition @ KPU
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Sample Size and Population Size
Example of a Confidence Interval
By definition, a confidence interval is a statistical range calculated around a sample statistic that is designed to contain which of the following a specified percentage of the time?
If a calculated confidence interval completely excludes a specific hypothetical population mean, a researcher can conclude that the sample mean is not statistically significantly different from that hypothetical value.
A cognitive psychologist is testing a new training method to determine its effect on reaction times. The average reaction time in the general population is known to be 400 milliseconds (ms). Match each of the following research results (presented as 95% Confidence Intervals) to the correct statistical conclusion regarding the training group's performance.
A researcher is analyzing the results of a psychological study and determines that the confidence interval is too wide to be useful. Arrange the following steps in the logical order that describes how the researcher's decision to increase the sample size leads to a more precise estimate.
A developmental psychologist is designing a mock-up of a research poster to teach students how to evaluate statistical findings. The goal is to create a hypothetical scenario where a new intervention's impact is judged to be 'statistically effective' compared to a baseline population mean of , but where the specific estimate of that impact remains highly uncertain (represented by a wide range). Which of the following result summaries should the psychologist construct to fulfill these spec
The most commonly used confidence interval in psychological research is set to contain the true population parameter of the time.
A student in an introductory psychology research methods course is learning about interval estimation. Match each component or outcome of a confidence interval with its correct conceptual interpretation.
A clinical psychologist is evaluating a claim that a specific mindfulness technique has no impact on stress levels (where a difference of indicates no impact). The researcher's study results in a confidence interval for the mean reduction in stress of [4.2, 10.8]. Because the value representing 'no impact' falls entirely outside this interval, the researcher should judge the initial claim as _____.
A social psychologist surveys 200 college students about daily social media use (in minutes) and obtains a confidence interval of [85, 115]. After examining the interval, the researcher notes that a media organization's claimed population mean of 130 falls completely _____ the interval, while a second published estimate of 95 falls completely inside it — leading the researcher to conclude that only the first claim is statistically refuted at the .05 level.
An undergraduate student completing a research methods paper must decide whether to report statistical results using only a null hypothesis test (p-value) or a confidence interval. Arrange the following steps of the student's evaluative reasoning in the most logical order.
Define a confidence interval and specify what factors determine its width (specifically comparing the role of sample size and population size).
Based on this scenario and the relationship between confidence intervals and null hypothesis tests, explain how the psychologist should evaluate the skeptic's claim. What conclusion should be made regarding the statistical significance of the difference between the sample mean and the hypothesized population mean of , and why?
A developmental psychologist surveys a sample of children and calculates a confidence interval of [47, 53] for the percentage of children who read daily, where the population size is one hundred thousand. If the psychologist conducts the same study with a sample of children from a population of one hundred million, what will the new confidence interval be, and why?
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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 ms. To create a report where a hypothesized population mean of 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 confidence interval ()?
In the provided example, a hypothetical population mean that falls within the range of the confidence interval ( to ) 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 , with a confidence interval ranging from to . When evaluating a hypothesis that predicts the true population mean is , 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 minutes per week, with a confidence interval of [, ] minutes. Match each hypothetical population mean to the correct conclusion about statistical significance at .
A researcher studying nightly sleep duration in college students finds a confidence interval of [, ] hours. The researcher concludes: 'Because hours falls inside the confidence interval, it is statistically significantly different from the sample mean at .' A student carefully evaluating this conclusion correctly judges it to be _____, because values inside a confidence interval are NOT considered statistically significantly different from the s
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 confidence interval range, and how a hypothetical population mean of 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 is statistically significantly different from the sample mean.
If a researcher obtains a sample mean of calories and a confidence interval of to for a cookie calorie estimation task, apply this information to evaluate the claim that the true population mean is . State whether this claim is statistically significantly different at the .05 alpha level and explain why.