tabita57i
2020-10-27
Answered

Sharing music online (5.2, 5.3). A sample survey reports that 29% of Internet users download music files online, 21% share music files from their computers, and 12% both download and share music. Make a two-way table that displays this information.

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Nathalie Redfern

Answered 2020-10-28
Author has **99** answers

We are interested in the proportion of Internet users that download music
files online and that share music files from their computers.

Let us name the columns of the two-way table "download online” and "do not download online”, while we name the rows of the two-way table "share music files” and "do not share music files”.

$\begin{array}{cccc}& \text{Download online}& \text{Do not download online}& \text{Total}\\ \text{Share music files}& & & \\ \text{Do not share music files}& & & \\ \text{Total}& & \end{array}$

29% of the Internet users download music files online, while 21% share music. files and 12% do both. We also know that the table needs to contain 100% of the Internet users in total.

The remaining percentages can be determined using the known row/column totals.

$\begin{array}{cccc}& \text{Download online}& \text{Do not download online}& \text{Total}\\ \text{Share music files}& 12\mathrm{\%}& 21\mathrm{\%}-12\mathrm{\%}=9\mathrm{\%}& 21\mathrm{\%}\\ \text{Do not share music files}& 29\mathrm{\%}-12\mathrm{\%}=17\mathrm{\%}& 71\mathrm{\%}-9\mathrm{\%}=62\mathrm{\%}& 100\mathrm{\%}-21\mathrm{\%}=79\mathrm{\%}\\ \text{Total}& 29\mathrm{\%}& 100\mathrm{\%}-29\mathrm{\%}=71\mathrm{\%}& 100\mathrm{\%}\end{array}$

Let us name the columns of the two-way table "download online” and "do not download online”, while we name the rows of the two-way table "share music files” and "do not share music files”.

29% of the Internet users download music files online, while 21% share music. files and 12% do both. We also know that the table needs to contain 100% of the Internet users in total.

The remaining percentages can be determined using the known row/column totals.

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A group of 125 truck owners were asked what brand of truck they owned and whether or not the truck has four-wheel drive. The results are summarized in the two-way table below. Suppose we randomly select one of these truck owners.

$\begin{array}{ccc}& \text{Four-wheel drive}& \text{No four-wheel drive}\\ \text{Ford}& 28& 17\\ \text{Chevy}& 32& 18\\ \text{Dodge}& 20& 10\end{array}$

What is the probability that the person owns a Dodge or has four-wheel drive?

$(a)\frac{20}{80}$

$(b)\frac{20}{125}$

$(c)\frac{80}{125}$

$(d)\frac{90}{125}$

$(e)\frac{110}{125}$

What is the probability that the person owns a Dodge or has four-wheel drive?

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Significance level for a hypothesis test for a linear regression

Consider linear regression model ${Y}_{i}=a+b\cdot {x}_{i}+{\u03f5}_{i}$, $i=1,2,3,4,5$ where $a,b\in \mathbb{R}$ are unknown and ${x}_{1}={x}_{2}=1,{x}_{3}=3,{x}_{4}={x}_{5}=5$, ${\u03f5}_{i}$ are iid, normally distributed with mean =0 and variance =9. Consider the hypothesis ${H}_{0}:b=0$ with the alternative ${H}_{1}:b\ne 0$, with the critical region $\{|\hat{b}|>c\}$, where b^ is a maximum likelihood estimator and c is chosen in such a way that the significance level of a test is equal to 0,05. Calculate c.

Could you help me with this exercise? It is taken from the actuary exam organized in my country. I thought that I am able solve this exercise, however my answer c=0,7528 is wrong, the correct answer is c=1,47.

Edited: the exercise seems very easy, but I'm sure that my method of solution is wrong, as I've seen the similar exercise and my method results with the wrong answer as well.

That's why I've decided to start a bounty, however I do not know how (I can see "question eligible for bounty in 59 minutes" only, not "start a bounty")

Consider linear regression model ${Y}_{i}=a+b\cdot {x}_{i}+{\u03f5}_{i}$, $i=1,2,3,4,5$ where $a,b\in \mathbb{R}$ are unknown and ${x}_{1}={x}_{2}=1,{x}_{3}=3,{x}_{4}={x}_{5}=5$, ${\u03f5}_{i}$ are iid, normally distributed with mean =0 and variance =9. Consider the hypothesis ${H}_{0}:b=0$ with the alternative ${H}_{1}:b\ne 0$, with the critical region $\{|\hat{b}|>c\}$, where b^ is a maximum likelihood estimator and c is chosen in such a way that the significance level of a test is equal to 0,05. Calculate c.

Could you help me with this exercise? It is taken from the actuary exam organized in my country. I thought that I am able solve this exercise, however my answer c=0,7528 is wrong, the correct answer is c=1,47.

Edited: the exercise seems very easy, but I'm sure that my method of solution is wrong, as I've seen the similar exercise and my method results with the wrong answer as well.

That's why I've decided to start a bounty, however I do not know how (I can see "question eligible for bounty in 59 minutes" only, not "start a bounty")

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