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You are studying the ages of people afflicted with acne. You collected a random sample of 49 people that have acne and recorded their ages. Using this data, you find that the sample mean age is 18.2 years and sample standard deviation is 18.3 years. Assume that the ages are normally distributed.

 

 

To find a 91% confidence interval for the ages of people with acne, what z-value would you need to use?

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Related textbook solutions

Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

Related questions

1. Mr. Jones is interested in determining how long it takes his students to write essays for his class. 

The table below shows the mean and standard deviation for the length of time to write an essay (in minutes) for a random sample of 20 AP Statistics students and a random sample of 25 physics Honors students. (These are from all students he has had through the years)

Based on the histogram of the data, it is not unreasonable to assume the distribution of essay times is approx normal.

a. Estimate the mean difference in essay completion times for all AP Statistics and Physics Honors students In Mr. Jone's classes.

b. Based only on this confidence interval, do you think the difference in the mean wait times is statistically significant? Justify your answer.

 

In mid-July, some businesses like to remind us that the holiday seasons are coming soon. Just like these businesses, the following questions will immerse you in the festive spirit and will (hopefully!) make you forget the heat waves. An article published in 2016 published the results of a survey on Canadians’ behaviour during this period. You are asked to answer the following questions

 

(a) From the data in the article, explain how we can show that the average amount planned to spend in 2016 for the group of 35+ years old is greater than $680,58 in the sample. Assume that there are 450 people that are between 18 and 34 years old in the sample.

(b) Using the article in reference, can we affirm that in 2016 the gap between the average amount planned to spend between the 18-34 years old and the 35+ years old is greater than 275 $ in the population, in favour of the 35+ years old? Assume the sample’s standard deviation is 150 $ among the 18-34 years old and that the sample’s standard deviation is 200 $ among the 35+ years old. You can also assume that the populations are normal. Use a significance level of α = 0, 01.

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You are studying the affect of financial means on students' average hours of sleep. You have found a reliable study indicating that students that have a job and do not receive financial support from their parents or guardians sleep an average of 5.8 hours per night (excluding weekends) on average (population average).
You decide to test whether or not students who do not work get more sleep per week night on average. You take a sample of 63 students that do not work and live with parents or guardians then you record the number of hours per week night they sleep for a period of 15 weeks (1 semester). You find that the average (mean) hours slept per week night in your sample is 7.2 hours and the standard deviation is 3.9 hours. Assume that average sleeping hours on week nights is normally distributed across students.
 
Remember to define the null and alternative hypotheses to help you answer the question.
 
What will the value of the test statistic (z-test) be?
(Round your answer to two decimal places)

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