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3 years ago

9

While shopping for clothes, Daniel spent $34 less than 3 times what Jaclyn spent. Daniel spent $14. Write and solve an equation

to find how much Jaclyn spent. Let x represent how much Jaclyn spent.
___x - ___ = ___

Jaclyn spent $____

1 answer:

topjm [15]3 years ago

4 0

Answer: Jaclyn spent $48

Step-by-step explanation:

3x - 34 = 14

3x = 14+34

X = 48/3 = 16

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Assume I created a 95% confidence interval for the mean hours studied for a test based on a random sample of 64 students. The lo

CaHeK987 [17]

Answer:

(a) Width = 15.4866.

(b) Margin of error = 7.7433.

(c) Center = 10.8849.

(d) Sample mean = 10.8849.

(e) <em>z</em> = 1.96.

(f) Population standard deviation = 31.6053.

Step-by-step explanation:

The (1 - <em>α</em>)% confidence interval for the population mean when the population standard deviation is known is:

$CI=\bar x\pm z_{\alpha/2}{\frac{\sigma}{\sqrt{n}}$

The 95% confidence interval for the mean hours studied for a test is (3.1416, 18.6282).

The sample taken was of size, <em>n</em> = 64.

(a)

Compute the width of the interval as follows:

$Width=Upper\ limit-Lower\ limit\\=18.6282-3.1416\\=15.4866$

Thus, the width of the confidence interval is 15.4866.

(b)

Compute the margin of error of the interval as follows:

$MOE=\frac{Width}{2}=\frac{15.4866}{2}=7.7433$

Thus, the margin of error of the confidence interval is 7.7433.

(c)

Compute the center of the confidence interval as follows:

$Center=\frac{Upper\ limit+Lower\ limit}{2}=\frac{18.6282+3.1416}{2}=10.8849$

Thus, the center of the confidence interval is 10.8849.

(d)

The center of a (1 - <em>α</em>)% confidence interval is the value of the sample statistic.

In case of the confidence interval for population mean the center of the interval is the sample mean.

The value of sample mean is 10.8849.

(e)

For a 95% confidence interval the critical value of <em>z</em> is:

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

*Use a <em>z</em>-table for the critical value.

Thus, the value of <em>z</em> is 1.96.

(f)

Compute the value of standard deviation as follows:

$MOE=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}\\7.7433=1.96\times \frac{\sigma}{\sqrt{64}}\\\sigma=\frac{7.7433\times 8}{1.96}\\\sigma=31.6053$

Thus, the value of population standard deviation is 31.6053.

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4 years ago

A random sample of 150recent donations at a certain

gtnhenbr [62]

Answer:

Null hypothesis: $p\geq 0.4$

Alternative hypothesis: $p < 0.4$

$z=\frac{0.3 -0.4}{\sqrt{\frac{0.4(1-0.4)}{150}}}=-2.5$

$p_v =2*P(Z$

If we compare the p value obtained and the significance level given $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that the true proportion is not significantly lower than 0.4 or 40% at 1% of significance.

Step-by-step explanation:

1) Data given and notation

n=150 represent the random sample taken

X=45 represent the people with type A blood

$\hat p=\frac{45}{150}=0.3$ estimated proportion of people with type A blood

$p_o=0.4$ is the value that we want to test

$\alpha=0.01$ represent the significance level

Confidence=99% or 0.99

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion of people type A blood is less than 0.4:

Null hypothesis: $p\geq 0.4$

Alternative hypothesis: $p < 0.4$

When we conduct a proportion test we need to use the z statisitc, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

3) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.3 -0.4}{\sqrt{\frac{0.4(1-0.4)}{150}}}=-2.5$

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.01$ . The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v =2*P(Z$

If we compare the p value obtained and the significance level given $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that the true proportion is not significantly lower than 0.4 or 40% at 1% of significance.

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3 years ago

dr. wong can see 9 patients in 3 hours, at this rate how long willl it take dr too see 72 patients? PLEASE HELP!!!

Nataly [62]

How many times must he see 9 in order to cover all 72 of them ? 72/9 = 8 . He has to see 9 patients 8 times, so he has to work 3 hours 8 times. 3x8=24 hours.

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if employees who make more money pay a higher percentage of their income to the government, this is known as what?

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Answer;

-Progressive tax

Explanation;

-According to this type of tax system, the taxes assessed are based on the taxable amount, and follow an increasing schedule. High-income earners pay more than low-income earners, and the tax rate, along with tax liability, increases as an individual or entity's wealth increases.

-Therefore; higher earners pay a higher percentage of taxes and more money in taxes than do lower-income earners .

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A new company is in the process of evaluating its customer service. The company offers two types of sales: (1) Internet sales an

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Answer:

$H_A: P_{\text{Internet}}-P_{\text{Store}} > 0.10$

Step-by-step explanation:

We are given the following in the question:

Let $P_{\text{Internet}}$ be the proportion of the internet sales and $P_{\text{Store}}$ be the proportion of the store sale.

Hypothesis:

We have to conduct a hypothesis to check that the Internet sales are more than 10 percent higher than store sales.

Thus, we can design the null and alternative hypothesis as:

$H_{0}: P_{\text{Internet}}-P_{\text{Store}}\leq 0.10\\H_A: P_{\text{Internet}}-P_{\text{Store}} > 0.10$

Alternate Hypothesis:

The alternate hypothesis states that the proportion of the internet sales is greater than the proportion of store sales by 10 percent.

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