Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

A clinical trial was conducted to lest the eflectiveness of a drug for treating insomnia in obler subjocts. Before treatment, 20 subjects had a mean wake time of 101.0 min. After treatment, the 20 subjects had a mean wake time of 78.7min and a standard deviation of 23.2min. Assume that the 20 sample values appear to be from a normally distributed population and construct a 90% confidence interval estimate of the mean wake time for a population with drug treatments. What does the resull suggest about the mean wake time of 101.0 min before the treatment? Does the drug appear fo be effective? Construct the 90% confidence interval estimate of the mean wake time for a population with the treatment. ◻_(min) < mu < ◻min (Round to one decimal place as neoded)

A clinical trial was conducted to lest the eflectiveness of a drug for treating insomnia in obler subjocts. Before treatment, 2020 subjects had a mean wake time of 101101.00 min. After treatment, the 2020 subjects had a mean wake time of 78.7 min 78.7 \mathrm{~min} and a standard deviation of 23.2 min 23.2 \mathrm{~min} . Assume that the 2020 sample values appear to be from a normally distributed population and construct a 90% 90 \% confidence interval estimate of the mean wake time for a population with drug treatments. What does the resull suggest about the mean wake time of 101101.00 min before the treatment? Does the drug appear fo be effective?\newlineConstruct the 90% 90 \% confidence interval estimate of the mean wake time for a population with the treatment.\newline \square{\min }<\mu<\square \min \newline(Round to one decimal place as neoded)

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Precalculusright chevron icon
Interpret confidence intervals for population meansright chevron icon

Full solution

Q. A clinical trial was conducted to lest the eflectiveness of a drug for treating insomnia in obler subjocts. Before treatment, 2020 subjects had a mean wake time of 101101.00 min. After treatment, the 2020 subjects had a mean wake time of 78.7 min 78.7 \mathrm{~min} and a standard deviation of 23.2 min 23.2 \mathrm{~min} . Assume that the 2020 sample values appear to be from a normally distributed population and construct a 90% 90 \% confidence interval estimate of the mean wake time for a population with drug treatments. What does the resull suggest about the mean wake time of 101101.00 min before the treatment? Does the drug appear fo be effective?\newlineConstruct the 90% 90 \% confidence interval estimate of the mean wake time for a population with the treatment.\newline□min⁡<μ<□min⁡ \square{\min }<\mu<\square \min \newline(Round to one decimal place as neoded)
  1. Identify Given Information: Identify the given information.\newlineWe have a sample size nn of 2020 subjects, a sample mean xˉ\bar{x} of 78.778.7 minutes, and a sample standard deviation ss of 23.223.2 minutes. We want to construct a 90%90\% confidence interval for the population mean wake time μ\mu after treatment.
  2. Determine Distribution: Determine the appropriate distribution to use.\newlineSince the sample size is less than 3030 and we do not know the population standard deviation, we use the t-distribution to construct the confidence interval.
  3. Find T-Value: Find the t-value that corresponds to a 90%90\% confidence level for a t-distribution with n−1n-1 degrees of freedom.\newlineFor a 90%90\% confidence interval and 1919 degrees of freedom (n−1=20−1n-1 = 20-1), we look up the t-value in a t-distribution table or use a calculator with inverse t-distribution functionality. The t-value for a two-tailed test at 90%90\% confidence is approximately 1.7291.729.
  4. Calculate SEM: Calculate the standard error of the mean (SEM).\newlineSEM=snSEM = \frac{s}{\sqrt{n}}\newlineSEM=23.220SEM = \frac{23.2}{\sqrt{20}}\newlineSEM≈23.24.472SEM \approx \frac{23.2}{4.472}\newlineSEM≈5.188SEM \approx 5.188
  5. Calculate ME: Calculate the margin of error (ME).\newlineME=t-value×SEMME = t\text{-}value \times SEM\newlineME=1.729×5.188ME = 1.729 \times 5.188\newlineME≈8.968ME \approx 8.968
  6. Construct Confidence Interval: Construct the confidence interval.\newlineLower limit = xˉ−ME\bar{x} - \text{ME}\newlineLower limit = 78.7−8.96878.7 - 8.968\newlineLower limit ≈69.7\approx 69.7 (rounded to one decimal place)\newlineUpper limit = xˉ+ME\bar{x} + \text{ME}\newlineUpper limit = 78.7+8.96878.7 + 8.968\newlineUpper limit ≈87.7\approx 87.7 (rounded to one decimal place)
  7. Interpret Results: Interpret the results.\newlineThe 9090\% confidence interval estimate for the mean wake time after treatment is between 69.769.7 minutes and 87.787.7 minutes. Since the interval does not include the mean wake time of 101.0101.0 minutes before treatment, this suggests that the drug treatment has effectively reduced the mean wake time.

More problems from Interpret confidence intervals for population means

Question
Michael surveyed 22 politicians from his state about their views on certain issues.\newlineIs this sample of citizens of the state likely to be biased?\newlineChoices:\newline[A]yes\newline[B]no
Get tutor helpright-arrow

Posted 7 months ago

Question
Read the following description of an experiment.\newlineA massage therapist has received complaints that the fragrance of her massage oil is unpleasant. She is testing whether a new oil will improve each clients' experience.\newlineThe massage therapist randomly sorts her clients into two groups. She massages 55 clients from the first group with the new oil and 55 from the other group with her usual oil. She asks all 1010 clients to rate their massages.\newlineIs this experiment statistically well designed?\newlineChoices:\newline[A]yes\newline[B]no
Get tutor helpright-arrow

Posted 7 months ago

Question
A random sample of 3535 four-door passenger vehicles had a mean gas mileage, in miles per gallon (mpg) (\mathrm{mpg}) , of 25.9mpg 25.9 \mathrm{mpg} . The estimate had a margin of error of 2.6mpg 2.6 \mathrm{mpg} at a 98% 98 \% confidence level. Of the following, which is the most plausible value for the true mean gas mileage of all four-door passenger vehicles?\newlineChoose 11 answer:\newline(A) 24mpg 24 \mathrm{mpg} \newline(B) 29mpg 29 \mathrm{mpg} \newline(C) 32mpg 32 \mathrm{mpg} \newline(D) 35mpg 35 \mathrm{mpg}
Get tutor helpright-arrow

Posted 8 months ago

Question
In a poll of 11,578578 randomly selected American adults, 44.8% 44.8 \% of the respondents said that airlines should allow in-flight calls on airplanes. The poll reported a margin of error of 2.5% 2.5 \% at a 95% 95 \% confidence level. Which of the following is most likely to be equal to the percentage of all American adults who would say that airlines should allow in-flight calls?\newlineChoose 11 answer:\newline(A) 40% 40 \% \newline(B) 43% 43 \% \newline(C) 48% 48 \% \newline(D) 95% 95 \%
Get tutor helpright-arrow

Posted 10 months ago

Question
Malik walked up and back down an empty 18 m 18 \mathrm{~m} long escalator at a constant rate. Since the escalator was going up at the time, it took him only 22.5 s 22.5 \mathrm{~s} . Going down took Malik 9090 s. Assume the escalator speed is constant.\newlineWhat was Malik's walking speed?\newlinems \frac{\mathrm{m}}{\mathrm{s}}
Get tutor helpright-arrow

Posted 8 months ago

Question
Two baseball players are warming up by throwing balls to the catcher. The two players are located 1010 yards apart, and the angle from each player to the catcher is 55∘55^{\circ} and 71∘71^{\circ}, respectively. What is the distance from the farthest baseball player to the catcher?\newlineA. 10.12510.125 yards\newlineB. 11.68711.687 yards\newlineC. 14.50114.501 yards\newlineD. 14.79014.790 yards
Get tutor helpright-arrow

Posted 8 months ago

Question
Select the outlier in the data set.\newline74,84,86,87,89,91,92,98,12674,84,86,87,89,91,92,98,126
Get tutor helpright-arrow

Posted 8 months ago

Question
Solve for p p .p8=79p=□\begin{array}{l}\frac{p}{8}=\frac{7}{9} \\p=\square\end{array}
Get tutor helpright-arrow

Posted 8 months ago

Question
Jelani needs to hire at least 1212 artists for an upcoming event. He needs to hire visual artists, who will be paid $300\$300 for the event, and performers, who will be paid $480\$480 for the event. His budget for paying the artists is no more than $6,000\$6,000. He must hire at least 44 visual artists and at least 33 performers. Which of the following does not satisfy all of the conditions described?\newlineChoose 11 answer:\newline(A) 44 visual artists and 1010 performers\newline(B) 88 visual artists and 88 performers\newline(C) $300\$30000 visual artists and 33 performers\newline(D) $300\$30022 visual artists and 44 performers
Get tutor helpright-arrow

Posted 8 months ago

Question
Factor.\newlinek2+9k+18k^2 + 9k + 18\newline____\newline
Get tutor helpright-arrow

Posted 8 months ago

View all (88)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant