2) The students in a class collected data on the number of minutes per

Hard times In June 2010, a random poll of 800 working men found that 9% had taken on a second job to help pay the bills. (www.ca

Phoenix [80]

Answer:

a) The 95% confidence interval would be given (0.0702;0.1098).

We can conclude that the true population proportion at 95% of confidence is between (0.0702;0.1098)

b) Since the confidence interval NOT contains the value 0.06 we have anough evidence to reject the claim at 5% of significance.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

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".

$p$ represent the real population proportion of interest

$\hat p =0.09$ represent the estimated proportion for the sample

n=800 is the sample size required

$z$ represent the critical value for the margin of error

Confidence =0.95 or 95%

Part a

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

The confidence interval would be given by this formula

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

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

The margin of error is given by :

$Me=z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

$Me=1.96 \sqrt{\frac{0.09(1-0.09)}{800}}=0.0198$

And replacing into the confidence interval formula we got:

$0.09 - 1.96 \sqrt{\frac{0.09(1-0.09)}{800}}=0.0702$

$0.09 + 1.96 \sqrt{\frac{0.108(1-0.09)}{800}}=0.1098$

And the 95% confidence interval would be given (0.0702;0.1098).

We can conclude that the true population proportion at 95% of confidence is between (0.0702;0.1098)

Part b

Since the confidence interval NOT contains the value 0.06 we have anough evidence to reject the claim at 5% of significance.

6 0

1 year ago

Mike and Ike are experts at pitching horseshoes. 70% of Mike's tosses are ringers. 67% of Ike's tosses are ringers. Suppose Mike

ahrayia [7]

Mike tosses 70%
Ike tosses 67%
Both tosses 50%

<span>Which of the following is closest to the probability that Ike's proportion is ringers is higher than Mike's for those tosses?
</span>
P(m) = 70/100
P(i) = 67/100
P(b) = 50/100

= P(b) * P(i)
= 50/100 * 67/100
= 0.335

The correct answer is letter D) 0.3745.

3 0

1 year ago

Yuri is thinking of a 4-digit whole number. He rounds his number to the nearest thousand. His answer is 4000, what is the smalle

konstantin123 [22]

Answer:

Smallest number = 3500

Step-by-step explanation:

Rounding of numbers involve replacing numbers with simpler numbers. In order to round a number to the nearest thousand, the last 3 digits of the number should be considered. If the last 3 digits are less than 500, the number is rounded down(the thousand figure is unaffected), but if the last 3 digits are greater or equal to 500, the number is rounded up.

In this case, Yuri is thinking of a 4-digit whole number and he rounds his number to the nearest thousand. Since his answer is 4000, the smallest number yuri could be thinking of would be 3500 and the highest number he could be thinking of is 4499.

Thus, the smallest number Yuri could be thinking of is 3500

6 0

2 years ago

Se the divergence theorem to calculate the surface integral s f · ds; that is, calculate the flux of f across s. f(x, y, z) = x2

pishuonlain [190]

$\mathbf f(x,y,z)=x^2\sin y\,\mathbf i+x\cos y\,\mathbf j-xz \sin y\,\mathbf k$
$\implies\nabla\cdot\mathbf f(x,y,z)=2x\sin y-x\sin y-x\sin y=0$

which means

$\displaystyle\iint_S\mathbf f(x,y,z)\,\mathrm dS=\iiint_R\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV=0$

8 0

2 years ago

Paul bakes loaves of bread and bread rolls in the ratio of 2:5. If he bakes 750 bread rolls, how many loaves will he bake? A rec

Zanzabum

Paul bakes 300 bread loaves. I don’t know the question you’re asking for the second question.

6 0

1 year ago

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