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balandron [24]
2 years ago
9

Researchers from Dartmouth Medical School conducted a study in 2003 to look at the connection between watching actors smoking in

movies and smoking initiation among adolescents. In the study, 6,522 U.S. adolescents ages 10-14 who had never tried smoking were randomly selected. Of those who subsequently tried smoking for the first time, 38% did so because of exposure to smoking in the movies. Estimate the proportion of all U.S. adolescents ages 10-14 who started smoking because of seeing actors smoke in movies by constructing a 95% confidence interval.
Mathematics
1 answer:
docker41 [41]2 years ago
8 0

Answer:

The 95% confidence interval for the proportion of adolescents who tried smoking for the first time because of exposure to smoking in the movies is (0.37, 0.40).

Step-by-step explanation:

A confidence interval is an interval estimate of the population parameter. The confidence interval has a certain probability of consisting the true value of the parameter.

The (1 - <em>α</em>) % confidence interval for the population proportion (<em>p</em>) is given by:

CI=\hat p\pm z_{\alpha/2}\times \sqrt{\frac{\hat p(1-\hat p)}{n}}

The information provided is:

n = 6522\\\hat p=0.38\\z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96

*Use a <em>z</em>-table for the critical value.

Construct the 95% confidence interval for the proportion of adolescents who tried smoking for the first time because of exposure to smoking in the movies as follows:

CI=\hat p\pm z_{\alpha/2}\times \sqrt{\frac{\hat p(1-\hat p)}{n}}\\=0.38\pm 1.96\times \sqrt{\frac{0.38(1-0.38)}{6522}}\\=0.38\pm 0.0118\\=(0.3682, 0.3918)\\\approx (0.37, 0.40)

Thus, the 95% confidence interval for the proportion of adolescents who tried smoking for the first time because of exposure to smoking in the movies is (0.37, 0.40).

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arsen [322]

Answer:

<h3>The correct expression is 1 Over 5 x Superscript minus 8 Baseline y Superscript minus 13 Baseline EndFraction</h3>

Step-by-step explanation:

Given the expression \frac{3x^{-6}y^{-3} }{15x^{2}y^{10}  }for x ≠ 0, y ≠ 0 to get the equivalent expression we will have to simplify the given expression.

\frac{3x^{-6}y^{-3} }{15x^{2}y^{10}  }\\= \frac{3}{15} x^{-6-2}y^{-3-10}\\ = \frac{3}{15}x^{-8}y^{-13}  \\ =\frac{1}{5}x^{-8}y^{-13}  \\

The correct expression is 1 Over 5 x Superscript minus 8 Baseline y Superscript minus 13 Baseline EndFraction

6 0
2 years ago
A rope is 66 feet long. It is cut into two pieces such that one piece is half the length of the other. What is the length of the
dedylja [7]
So if one bit of the length, is half the size of the other bit then we can make the following equation, for x being the length of rope:

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That is the length, of the smaller one (half the big one), so 2x = 44. Hence d) is your answer.

Hope I helped!
7 0
2 years ago
Read 2 more answers
If one worker can assemble 9 products per hour, and another worker can assemble 6 products per hour, how long will it take them
leva [86]

Answer:

  3 hours 20 minutes

Step-by-step explanation:

Together, the workers can assemble 9 + 6 = 15 products per hour. So the assembly of 50 products will take ...

  (50 products)/(15 products/hour) = 50/15 hours = 3 1/3 hours

The two workers can assemble 50 products in 3 1/3 hours.

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2 years ago
A cake manufacturer boxes Swiss chocolate and German chocolate cakes at one site. A box of Swiss chocolate cake contains 0.55 lb
Kobotan [32]

Answer:

2,500 German chocolate cake boxes.

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Step-by-step explanation:

Let 'S' be the number of Swiss chocolate cakes boxed and 'G' the number of German cholocate cakes boxed. If all of the available ingredients are used:

0.55*S +0.59*G = 2,300\\0.45*S+0.41*G = 1,700

Solving the linear system above:

(0.55 *S +0.59*G)- \frac{0.55}{0.45} (0.45*S+0.41*G)= 2,300-\frac{0.55}{0.45}*1,700*\\0.088888*G = 222.222\\G=2,500\\S =\frac{2,300-2,500*0.59}{0.55}\\S=1500

2,500 German chocolate cake boxes and 1,500 Swiss chocolate cake boxes can be made each day.

6 0
2 years ago
Izumi is running on a quarter-mile oval track. After running 110 yards, his coach records his time as 16 seconds.
pickupchik [31]

Answer:

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Step-by-step explanation:

The problem is asking for Izumi's speed. The formula of speed is:

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The problem is also asking for the unit<u> miles per hou</u>r (\frac{miles}{hour}) so, this means that we have to know how many miles Izumi ran, given that the problem only mentioned<u> yards (110 yards).</u>

Let's convert 110 yards to miles, provided that he Izumi ran 1,760 yards in a mile.

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Let's go back again to the formula: s = \frac{d}{t}

s = \frac{0.0625 miles}{16 seconds} = 0.0039 \frac{miles}{sec}

Since, the we arrived at a miles per second unit, we have to convert it to miles per hour.

So, if a minute has 60 seconds, then an hour has 3,600 seconds.

Thus, 0.0039 \frac{miles}{sec} × 3,600 \frac{seconds}{hour} = 14.04 miles per hour (the answer)

3 0
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