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2 years ago

13

there were 138 students and 32 adults at a concert if 85% of the seats were filled how many seats are in the auditorium round yo

ur answer to the nearest percent

1 answer:

natta225 [31]2 years ago

8 0

Answer:

200 seats

Step-by-step explanation:

You might be interested in

In a random sample of 75 American women age 18 to 30, 26 agreed with the statement that a woman should have the right to a legal

ddd [48]

Answer:

a) $z=\frac{0.347-0.328}{\sqrt{0.338(1-0.338)(\frac{1}{75}+\frac{1}{64})}}=0.236$

$p_v =2*P(Z>0.236)=0.813$

If we compare the p value and using any significance level for example $\alpha=0.01$ always $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say that we don't have significant differences between the two proportions.

b) We are confident at 99% that the difference between the two proportions is between $-0.188 \leq p_B -p_A \leq 0.226$

Step-by-step explanation:

Previous concepts and data given

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 of women age 18 to 30 agreed with the statement that a woman should have the right to a legal abortion for any reason

$\hat p_A =\frac{26}{75}=0.347$ represent the estimated proportion of women age 18 to 30 agreed with the statement that a woman should have the right to a legal abortion for any reason

$n_A=75$ is the sample size for A

$p_B$ represent the real population proportion for women age 58 to 70 agreed with the statement that a woman should have the right to a legal abortion for any reason

$\hat p_B =\frac{21}{64}=0.328$ represent the estimated proportion of women age 58 to 70 agreed with the statement that a woman should have the right to a legal abortion for any reason

$n_B=64$ is the sample size required for B

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

The population proportion have the following distribution

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

Part a

We need to conduct a hypothesis in order to check if the proportion are equal, the system of hypothesis would be:

Null hypothesis: $p_{A} = p_{B}$

Alternative hypothesis: $p_{A} \neq p_{B}$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{A}-p_{B}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{A}}+\frac{1}{n_{B}})}}$ (1)

Where $\hat p=\frac{X_{A}+X_{B}}{n_{A}+n_{B}}=\frac{26+21}{75+64}=0.338$

Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.347-0.328}{\sqrt{0.338(1-0.338)(\frac{1}{75}+\frac{1}{64})}}=0.236$

Statistical decision

Since is a two sided test the p value would be:

$p_v =2*P(Z>0.236)=0.813$

If we compare the p value and using any significance level for example $\alpha=0.01$ always $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say that we don't have significant differences between the two proportions.

Part b

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 99% confidence interval the value of $\alpha=1-0.99=0.01$ and $\alpha/2=0.005$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=2.58$

And replacing into the confidence interval formula we got:

$(0.347-0.328) - 2.58 \sqrt{\frac{0.347(1-0.347)}{75} +\frac{0.328(1-0.328)}{64}}=-0.188$

$(0.347-0.328) + 2.58 \sqrt{\frac{0.347(1-0.347)}{75} +\frac{0.328(1-0.328)}{64}}=0.226$

And the 99% confidence interval for the difference of proportions would be given (-0.188;0.226).

We are confident at 99% that the difference between the two proportions is between $-0.188 \leq p_B -p_A \leq 0.226$

5 0

3 years ago

Please help me with these two questions!! show work too!

const2013 [10]

Answer:

x 37 y 30

Step-by-step explanation:

hopes it helps yo

4 0

2 years ago

Rewrite exponential expressions

Dahasolnce [82]

Answer:

A = 48

Step-by-step explanation:

In this equation, we can factor out the expression $(\frac{1}{7} )^x$ . If we do so, the expression becomes:

$(\frac{1}{7})^x((\frac{1}{7})^{-2} - 1)$

We can simplify to get:

$(\frac{1}{7} )^x(49 - 1)$

and get:

$48*(\frac{1}{7})^x$

Therefore, A = 48

8 0

2 years ago

Machine 1 can complete a task in x hours while an upgraded machine (machine 2) needs 9 fewer hours. The plant manager knows the

lara31 [8.8K]

The (0, 3] is taken out of the picture leaving you with B.

We have given that,

Machine 1 can complete a task in x hours while an upgraded machine (machine 2) needs 9 fewer hours.

We have to determine the,

The plant manager knows the two machines will take at least 6 hours, as represented by the inequality

after you find the intervals.

you also need to consider that the plant manager knows the two machines will take at least 6 hours.

so (0, 3] is taken out of the picture leaving you with B.

To learn more about the inequality visit:

brainly.com/question/24372553

#SPJ1

4 0

2 years ago

Solve 5 ÷ 2 5/7<br><br>10 5/7 <br><br>13 1/2 <br><br>1 8/9<br><br>1 16/19<br><br>

aivan3 [116]

1) 1.7857142857

2) 7.142857143

6 0

2 years ago