The function f is given by f(x) = 3x² - 5 - a) Work out f '(43)

Many high school students take the AP tests in different subject areas. In 2007, of the 144,796 students who took the biology ex

Nataly [62]

Answer:

$(0.582-0.485) - 1.64 \sqrt{\frac{0.582(1-0.582)}{144796} +\frac{0.485(1-0.485)}{211693}}=0.0942$

$(0.582-0.485) + 1.64 \sqrt{\frac{0.582(1-0.582)}{144796} +\frac{0.485(1-0.485)}{211693}}=0.09978$

And the 90% confidence interval would be given (0.0942;0.09978).

We are confident at 90% that the difference between the two proportions is between $0.0942 \leq p_A -p_B \leq 0.09978$

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".

$p_A$ represent the real population proportion female for Biology

$\hat p_A =\frac{84199}{144796}=0.582$ represent the estimated proportion female for biology

$n_A=144796$ is the sample size for A

$p_B$ represent the real population proportion female for calculus AB

$\hat p_B =\frac{102598}{211693}=0.485$ represent the estimated proportion female for Calculus AB

$n_B=211693$ is the sample size required for B

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

The population proportion have the following distribution

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

The confidence interval for the difference of two proportions would be given by this formula

$(\hat p_A -\hat p_B) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}$

For the 90% confidence interval the value of $\alpha=1-0.90=0.1$ and $\alpha/2=0.05$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.64$

And replacing into the confidence interval formula we got:

$(0.582-0.485) - 1.64 \sqrt{\frac{0.582(1-0.582)}{144796} +\frac{0.485(1-0.485)}{211693}}=0.0942$

$(0.582-0.485) + 1.64 \sqrt{\frac{0.582(1-0.582)}{144796} +\frac{0.485(1-0.485)}{211693}}=0.09978$

And the 90% confidence interval would be given (0.0942;0.09978).

We are confident at 90% that the difference between the two proportions is between $0.0942 \leq p_A -p_B \leq 0.09978$

5 0

3 years ago

Suppose you are determining whether the depth of groves cut into aluminum by a milling machine is equal to 1.7 mm. You cut 14 gr

Gemiola [76]

Answer:

For this case we want to check if the true mean for the depth of groves cut into aluminium by a machine is equal to 1.7 (null hypothesis) and the alternative hypothesis would be the complement different from 1.7. And the best system of hypothesis are:

Null hypothesis: $\mu =1.7$

Alternative hypothesis $\mu \neq 1.7[/tx]And the best system of hypothesis are:3. This two-sided test:
H0: μ = 1.7 mm
H1: μ ≠ 1.7 mmStep-by-step explanation:For this case we want to check if the true mean for the depth of groves cut into aluminium by a machine is equal to 1.7 (null hypothesis) and the alternative hypothesis would be the complement different from 1.7. And the best system of hypothesis are:Null hypothesis: [tex]\mu =1.7$

Alternative hypothesis [tex]\mu \neq 1.7[/tx]

And the best system of hypothesis are:

3. This two-sided test:

H0: μ = 1.7 mm

H1: μ ≠ 1.7 mm

4 0

3 years ago

Tommy and his friend went to go buy pie at Delicious Orchards. After paying seven dollars for the pie, Tommy

wlad13 [49]

Answer:

$102

Step-by-step explanation:

if Tommy spent 7 dollars on pie, that means he had more money than that amount before.

So before he spent 7 dollars, he had those 7 dollars.

Add 7 with 95

95 + 7 = 102

5 0

2 years ago

If a farmer sells 9.8 KL of apples and pears at the farmers market. 4/5 of this weight is apples,and the rest are pears. How man

faltersainse [42]

Answer:

1.96

Step-by-step explanation:

A farmer sells 9.8 kl of apples and pears

4/5 of this weight is apples, while the rest are pears

Therefore the wight of pears can be calculated as follows

Let x represent the weight of pears

9.8= 4/5×9.8 + x

9.8= 0.8×9.8+x

9.8= 7.84+x

9.8-7.84= x

x= 1.96

8 0

3 years ago

What is the slope from the coordinate points (2,6) (1,9)

Hunter-Best [27]

Answer:

$m=-3$

General Formulas and Concepts:

Pre-Alg

Order of Operations: BPEMDAS

Alg I

Slope Formula: $m=\frac{y_2-y_1}{x_2-x_1}$

Step-by-step explanation:

Step 1: Define

Point (2, 6)

Point (1, 9)

Step 2: Find slope m

Substitute: $m=\frac{9-6}{1-2}$
Subtract: $m=\frac{3}{-1}$
Divide: $m=-3$

8 0

2 years ago

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