What is x if the volume of the box is 70 in3

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

Last year Boris paid £256 for his car insurance.

jenyasd209 [6]

Answer:

The percentage increase in the cost of Boris car insurance cost is 249%

Step-by-step explanation:

In this question, we want to calculate the percentage increase in the cost of car insurance paid by Boris

Mathematically, to calculate this percentage increase, we shall need to make use of a mathematical formula.

Mathematically, the percentage increase would be;

{(new value paid-old value paid)/old value paid} * 100%

From the question, we can identify that the old value paid is £256 while the new value paid is £894

Thus, the percentage increase would be ;

(894-256)/256 * 100% = 638/256 * 100 = 2.4921875 * 100 = 249.21875 which is 249% increase to the nearest whole percentage

6 0

2 years ago

Alicia borrowed $15,000 to buy a car. She borrowed the money at 8% for 6 years. What is the interest she will pay for the loan ?

kykrilka [37]

The interest rate she would pay would be is $7,200

5 0

2 years ago

In a recent survey, the proportion of adults who indicated mystery as their favorite type of book was 0.325. Two simulations wil

Virty [35]

Answer:

C) The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B.

Step-by-step explanation:

The center for Simulation A and Simulation B will be roughly equal.

Overall Sample size of Simulation A = 1500 * 100 = 150000

Overall Sample size of Simulation B = 2000 * 50 = 100000

Since the sample size for Simulation A is greater, the variability of Simulation will be less.

Therefore, The answer is C) The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B.

3 0

2 years ago

Brahmagupta solved a quadratic equation of the form ax2 + bx = c using the formula x =, which involved only one solution. Using

weeeeeb [17]

X2+7x-8=0
product=-8 times 1 = -8
sum= 7
{-1, 8}
x2-1x+8x-8=0
x(x-1)+8(x-1)=0
x+8=0 or X-1=0
x=-8

4 0

1 year ago

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