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LiRa [457]
3 years ago
11

Suppose that a random sample of 50 bottles of a particular brand of cough syrup is selected and the alcohol content of each bott

le is determined. Let m denote the average alcohol content for the population of all bottles of the brand under study. Suppose that the resulting 95% confidence interval is (7.8, 9.4). a. Would a 90% confidence interval calculated from this same sample have been narrower or wider than the given interval
Mathematics
1 answer:
timofeeve [1]3 years ago
6 0

Answer:

95% confidence interval will be narrower.

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 50

95% confidence interval for average alcohol content:

(7.8, 9.4)

a) 90% confidence interval

  • If we calculate a 90% confidence interval, then the confidence interval become narrower because we decreased the confidence percentage.
  • This would decrease the margin of error.
  • Hence, the confidence interval become narrower.
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Suppose that the population of the scores of all high school seniors who took the SAT Math (SAT-M) test this year follows a Norm
Vlad1618 [11]

Answer:

Confidence =1-\alpha=1-0.01=0.99

And then the confidence level would be given by 99%

Step-by-step explanation:

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Assuming the X follows a normal distribution

X \sim N(\mu, \sigma)

The distribution for the sample mean is given by:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

\bar x =512 represent the sample mean

\sigma=100 represent the population standard deviation

n= 100 sample size selected.

The confidence interval is given by this formula:

\bar X \pm z_{\alpha/2} \frac{\sigma}{\sqrt{n}}   (1)

The marginof error for this case is given by Me=25.76. And we know that the formula for the margin of error is given by:

Me=z_{\alpha/2} \frac{\sigma}{\sqrt{n}}

25.76=z_{\alpha/2} \frac{100}{\sqrt{100}}

And we can find the critical value z_{\alpha/2} like this:

z_{\alpha/2}=\frac{25.76(\sqrt{100})}{100}=2.576

And we know that on the right tail of the z score =2.576 we have \alpha/2 of the total area. We can find the area on the right of the z score using this excel code:

"=1-NORM.DIST(2.576,0,1,TRUE)" or using a table of the normal standard distribution, and we got 0.004998=\alpha/2, so then \alpha=0.00498*2=0.009995 \approx 0.01, and then we can find the confidence like this:

Confidence =1-\alpha=1-0.01=0.99

And then the confidence level would be given by 99%

8 0
3 years ago
James used base-ten to show that 40 is one-tenth of 400. Explain your reasoning
Elanso [62]
Cause 400 divided by 10 is 40

3 0
3 years ago
A group of friends were working on a student film. They spent all their budget on
Sophie [7]

Answer:

$820

Step-by-step explanation:

Total = Equipment + Props

T = 369 + 0.55T

0.45T = 369

<u>T = 820</u>

I hope this helps!

4 0
2 years ago
Iteration - Maths Question attached
Ivanshal [37]

Answer:

7.8

Step-by-step explanation:

First I will try 50. I got 127,550, so that was way too big.

Let me try a smaller number. How about 5. I got 155, so that was a bit too small.

Now I'll try 20. I got 8420. Looks like the number is between 5 and 20.

How about 7. I got 399.

Let me try 8. I got 584! That's really close. It's just a little too big.

I tried 7.5, and got 485.624. So close! Just a little higher.

Putting in 7.8 yields <u>543.192!</u> That's our answer.

8 0
3 years ago
Wesley jogs 10 miles each weeks. Then he jogs 20 miles each week for 3 weeks how many miles does Wesley jog in 5 week?
Kruka [31]
I think he would jog 80 miles in 5 weeks
20+20+20+10+10=80
6 0
3 years ago
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