a) The 99% CI for the true proportion of voters who prefer the Republican candidate is (0.3658, 0.6001). This means that we are 99% sure that the true population proportion of all voters who prefer the Republican candidate is (0.3658, 0.6001).

b) The upper bound of the confidence interval is above 0.5 = 50%, which meas that the candidate can be confidence of victory.

Step-by-step explanation:

Question a:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

Sample of 120 registered voters in order to predict the winner of a local election. The Democrat candidate was favored by 62 of the respondents.

So 120 - 62 = 58 favored the Republican candidate, so:

$n = 120, \pi = \frac{58}{120} = 0.4833$

99% confidence level

So $\alpha = 0.01$ , z is the value of Z that has a p-value of $1 - \frac{0.01}{2} = 0.995$ , so $Z = 2.575$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4833 - 2.575\sqrt{\frac{0.4833*0.5167}{120}} = 0.3658$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4833 + 2.575\sqrt{\frac{0.4833*0.5167}{120}} = 0.6001$

The 99% CI for the true proportion of voters who prefer the Republican candidate is (0.3658, 0.6001). This means that we are 99% sure that the true population proportion of all voters who prefer the Republican candidate is (0.3658, 0.6001).

b. If a candidate needs a simple majority of the votes to win the election, can the Republican candidate be confident of victory? Justify your response with an appropriate statistical argument.

The upper bound of the confidence interval is above 0.5 = 50%, which meas that the candidate can be confidence of victory.

8 0

3 years ago

How many 3 3/4 inch wires can be cut from a spool if wire that is 100 inches how much will be left over

Akimi4 [234]

How many 3 $\frac{3}{4}$ wires can be cut from a spool of wire that is 100 inches long?

How many inches will be left over?

Number of pieces of wires = length of spool of wire ÷ length of each piece of wire.

Number of pieces = 100 ÷ 3 $\frac{3}{4}$ = 100 ÷ $\frac{15}{4}$

That gives $\frac{100 * 4}{15}$

Simplifying gives $\frac{400}{15}$ = $\frac{80}{3}$

This is equivalent to 26 $\frac{2}{3}$ pieces

So 26 pieces of wires can be cut from a spool and $\frac{2}{3}$ of a piece will be left over.

6 0

3 years ago

Which equation represents the line shown

murzikaleks [220]

Answer: Third option:

Step-by-step explanation:

The equation in Slope Intercept form of a line that does not pass through the point (0,0), which is known as "Origin, is the following:

$y=mx+b$

Where "m" is the slope of the line and "b" is the y-intercept.

The equation in Slope Intercept form of a line that passes through the Origin, is:

$y=mx$

Where "m" is the slope of the line.

In this case you can observe in the picture attached that the line passes through the point (0,0).

You can also notice that "y" would be the Dependent variable and "x" the Independent variable.

Therefore, the equation of this must have this form:

$y=mx$

The only equation that matches with that form, is the one given in the Third option. This is:

$y=2x$

7 0

3 years ago