Which sampling method is generally the weakest

Area= 7 1/4 x 11 2/3

Vesna [10]

Answer:

Area=84.5833333333

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Stephanie took a science exam that had two parts. Part 1: She got 16 questions correct, which was 45 of the number of part 1 que

vesna_86 [32]

Given :

Stephanie took a science exam that had two parts. Part 1: She got 16 questions correct, which was 4/5 of the number of part 1 questions. Part 2: She got 16 questions correct, which was 2/3 of the number of part 2 questions.

To Find :

The total number of questions on Stephanie's exam.

Solution :

Let, number of questions in Part 1 is x :

$16=\dfrac{4}{5}x\\\\x=20$

Let, number of questions in Part 2 is y :

$16=\dfrac{2}{3}y\\\\y=24$

Therefore, total number of questions on Stephanie's exam are 20 + 40 = 60.

Hence, this is the required solution.

5 0

3 years ago

Two catalysts may be used in a batch chemical process. Twelve batches were prepared using catalyst 1, resulting in an average yi

aalyn [17]

Answer:

a) $t=\frac{(91-85)-(0)}{2.490\sqrt{\frac{1}{12}}+\frac{1}{15}}=6.222$

$df=12+15-2=25$

$p_v =P(t_{25}>6.222) =8.26x10^{-7}$

So with the p value obtained and using the significance level given $\alpha=0.01$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis.

b) $(91-85) -2.79 *2.490 \sqrt{\frac{1}{12} +\frac{1}{15}} =3.309$

$(91-85) +2.79 *2.490 \sqrt{\frac{1}{12} +\frac{1}{15}} =8.691$

Step-by-step explanation:

Notation and hypothesis

When we have two independent samples from two normal distributions with equal variances we are assuming that

$\sigma^2_1 =\sigma^2_2 =\sigma^2$

And the statistic is given by this formula:

$t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{S_p\sqrt{\frac{1}{n_1}}+\frac{1}{n_2}}$

Where t follows a t distribution with $n_1+n_2 -2$ degrees of freedom and the pooled variance $S^2_p$ is given by this formula:

$\S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}$

This last one is an unbiased estimator of the common variance $\sigma^2$

Part a

The system of hypothesis on this case are:

Null hypothesis: $\mu_2 \leq \mu_1$

Alternative hypothesis: $\mu_2 > \mu_1$

Or equivalently:

Null hypothesis: $\mu_2 - \mu_1 \leq 0$

Alternative hypothesis: $\mu_2 -\mu_1 > 0$

Our notation on this case :

$n_1 =12$ represent the sample size for group 1

$n_2 =15$ represent the sample size for group 2

$\bar X_1 =85$ represent the sample mean for the group 1

$\bar X_2 =91$ represent the sample mean for the group 2

$s_1=3$ represent the sample standard deviation for group 1

$s_2=2$ represent the sample standard deviation for group 2

First we can begin finding the pooled variance:

$\S^2_p =\frac{(12-1)(3)^2 +(15 -1)(2)^2}{12 +15 -2}=6.2$

And the deviation would be just the square root of the variance:

$S_p=2.490$

Calculate the statistic

And now we can calculate the statistic:

$t=\frac{(91-85)-(0)}{2.490\sqrt{\frac{1}{12}}+\frac{1}{15}}=6.222$

Now we can calculate the degrees of freedom given by:

$df=12+15-2=25$

Calculate the p value

And now we can calculate the p value using the altenative hypothesis:

$p_v =P(t_{25}>6.222) =8.26x10^{-7}$

Conclusion

So with the p value obtained and using the significance level given $\alpha=0.01$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis.

Part b

For this case the confidence interval is given by:

$(\bar X_1 -\bar X_2) \pm t_{\alpha/2} S_p \sqrt{\frac{1}{n_1} +\frac{1}{n_2}}$

For the 99% of confidence we have $\alpha=1-0.99 = 0.01$ and $\alpha/2 =0.005$ and the critical value with 25 degrees of freedom on the t distribution is $t_{\alpha/2}= 2.79$

And replacing we got:

$(91-85) -2.79 *2.490 \sqrt{\frac{1}{12} +\frac{1}{15}} =3.309$

$(91-85) +2.79 *2.490 \sqrt{\frac{1}{12} +\frac{1}{15}} =8.691$

7 0

3 years ago

Given f(x) = x2 + 4x − 1 and g(x) = 5x − 7, identify (fg)(x).

8_murik_8 [283]

<span> f(x) = x^2 + 4x − 1 and g(x) = 5x − 7
</span>(fg)(x) = (x^2 + 4x − 1)(5x − 7)
(fg)(x) = 5x^3 + 20x^2 - 5x - 7x^2 - 28x + 7
(fg)(x) = 5x^3 + 13x^2 - 33x + 7

answer is C. third choice

(fg)(x) = 5x^3 + 13x^2 - 33x + 7

4 0

3 years ago

I don’t know how to solve for Q.

Naya [18.7K]

Answer:

∠Q = 75°

Step-by-step explanation:

Start by recognizing that the triangle is isosceles (the long sides are marked as being equal-length). That means angles Q and R have the same measure.

Next, you use the fact that the sum of angles is 180° to write an equation.

∠R +∠P +∠Q = 180°

(2x +15)° +x° +(2x +15)° = 180° . . . . substitute the known values

5x +30 = 180 . . . . . . . . . . . . . . . . divide by °, collect terms

5x = 150 . . . . . . . . subtract 30

x = 30 . . . . . . . divide by 5

Then angle Q is ...

∠Q = (2x +15)° = (2×30 +15)°

∠Q = 75°

8 0

2 years ago