STT 212 Lecture Notes - Lecture 17: Standard Deviation, Gifted Education

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peachwoodchuck721

16 Apr 2019

School

University of Rochester

Department

Statistics

Course

STT 212

Professor

Mcdermott

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Document Summary

The standard deviation is a measure of the spread of scores within a set of data. Usually, we are interested in the standard deviation of a population. However, as we are often presented with data from a sample only, we can estimate the population standard deviation from a sample standard deviation. These two standard deviations - sample and population standard deviations - are calculated differently. In statistics, we are usually presented with having to calculate sample standard deviations, and so this is what this article will focus on, although the formula for a population standard deviation will also be shown. When to use the sample or population standard deviation. We are normally interested in knowing the population standard deviation because our population contains all the values we are interested in. However, in statistics, we are usually presented with a sample from which we wish to estimate (generalize to) a population, and the standard deviation is no exception to this.

Related Questions

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.

(c) Build and interpret a 98 % confidence interval that estimates the gap between the average amount planned to spend between the 18-34 years old and the 35+ years old in 2016. Could we use this interval to find the conclusion of the hypothesis test performed in (b)?

maroonraccoon733

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)

amaranthrabbit32

A -one-tailed hypothesis test with the t statistic:

Antisocial personality disorder (ASPD) is characterized by deceitfulness, reckless disregard for the well-being of others, a diminished capacity for remorse, superficial charm, thrill-seeking, and poor behavioral control. ASPD is not normally diagnosed in children or adolescents, but antisocial tendencies can sometimes be recognized in childhood or early adolescence. James Blair and his colleagues have studied the ability of children with antisocial tendencies to recognize facial expressions that depict sadness, happiness, anger, disgust, fear, and surprise. They have found that children with antisocial tendencies have selective impairments, with significantly more difficulty recognizing fearful and sad expressions.

Suppose you have a sample of 45 children with antisocial tendencies and you are particularly interested in the emotion of fear. You find that while the average 14-year-old has a score of 13.85 on the emotion recognition scale, your sample of 14-year-old children with antisocial tendencies has an average score of 14.60 with a standard deviation of 2.96. A higher score represents that it took a higher degree of emotional expression for the child to correctly identify the emotion of fear, indicating greater difficulty recognizing the emotion. Assume that scores on the emotion recognition scale are normally distributed.

The null hypothesis is that your sample of children with antisocial tendencies would have no more difficulty recognizing emotion hat the general population of 14-year-olds. Stated using symbols.......

tailored test. Given what you know, you will evaluate this hypothesis using a ...........statistic.

plumgoldfish158

STT 212 Lecture Notes - Lecture 17: Standard Deviation, Gifted Education

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