Best deal?2oz for 4.99 or 6oz for 9.85

A dairy farmer distributes 660 ounces of milk products each day. The milk is packaged in 12-ounce containers. Find the number o

abruzzese [7]

55 containers were distributed each day

12(55)=660

3 0

3 years ago

Read 2 more answers

Test the claim that the mean GPA of night students is larger than 2 at the .025 significance level. The null and alternative hyp

exis [7]

Answer:

$H_0: \, \mu = 2$ .

$H_1:\, \mu > 2$ .

Test statistics: $z \approx 2.582$ .

Critical value: $z_{1 - 0.025} \approx 1.960$ .

Conclusion: reject the null hypothesis.

Step-by-step explanation:

The claim is that the mean $\mu$ is greater than $2$ . This claim should be reflected in the alternative hypothesis:

$H_1:\, \mu > 2$ .

The corresponding null hypothesis would be:

$H_0:\, \mu = 2$ .

In this setup, the null hypothesis $H_0:\, \mu = 2$ suggests that $\mu_0 = 2$ should be the true population mean of GPA.

However, the alternative hypothesis $H_1:\, \mu > 2$ does not agree; this hypothesis suggests that the real population mean should be greater than $\mu_0= 2$ .

One way to test this pair of hypotheses is to sample the population. Assume that the population mean is indeed $\mu_0 = 2$ (i.e., the null hypothesis is true.) How likely would the sample (sample mean $\overline{X} = 2.02$ with sample standard deviation $s = 0.06$ ) be observed in this hypothetical population?

Let $\sigma$ denote the population standard deviation.

Given the large sample size $n = 60$ , the population standard deviation should be approximately equal to that of the sample:

$\sigma \approx s = 0.06$ .

Also because of the large sample size, the central limit theorem implies that $Z= \displaystyle \frac{\overline{X} - \mu_0}{\sigma / \sqrt{n}}$ should be close to a standard normal random variable. Use a $Z$ -test.

Given the observation of $\overline{X} = 2.02$ with sample standard deviation $s = 0.06$ :

$\begin{aligned}z_\text{observed}&= \frac{\overline{X} - \mu_0}{\sigma / \sqrt{n}} \\ &\approx \frac{\overline{X} - \mu_0}{s / \sqrt{n}} = \frac{2.02 - 2}{0.06 / \sqrt{60}} \approx 2.582\end{aligned}$ .

Because the alternative hypothesis suggests that the population mean is greater than $\mu_0 = 2$ , the null hypothesis should be rejected only if the sample mean is too big- not too small. Apply a one-sided right-tailed $z$ -test. The question requested a significant level of $0.025$ . Therefore, the critical value $z_{1 - 0.025}$ should ensure that $P( Z > z_{1 - 0.025}) = 0.025$ .

Look up an inverse $Z$ table. The $z_{1 - 0.025}$ that meets this requirement is $z_{1 - 0.025} \approx 1.960$ .

The $z$ -value observed from the sample is $z_\text{observed}\approx 2.582$ , which is greater than the critical value. In other words, the deviation of the sample from the mean in the null hypothesis is sufficient large, such that the null hypothesis needs to be rejected at this $0.025$ confidence level in favor of the alternative hypothesis.

3 0

3 years ago

The length of a rectangular picture frame is twice it's width. We know that the perimeter of the rectangular frame is less than

I am Lyosha [343]

For the first part:
if w is width and length is 2 times that, what would the length be?

For the second part:
we know that the perimeter is less-than 48in, so we can start by saying
something<48
next you have to determine what that something is: the perimeter.
To find perimeter, you add the length of the sides. We already know that there are two sides which measure 'w' units, and two sides which measures are the expression you're finding in the first part. So, you simply need to add these together!
width + width + length + length<48.
(Note: you'll obviously want to replace the words width and length with the values for the width and length; in the case of width, the value is given in the problem in the form of a variable, and the length is the expression you solve for in the first part.

You should be able to solve to find the expression from the first part on your own, and once you have those, simply plug the value of the width and the length into the expression. Rather than just giving you the answer, this allows you to still work it out on your own to a certain extent.

Make sense? (:

4 0

3 years ago

Find the slope of the line going through the points (0,6) and (-3,9)

andre [41]

Answer:

The slope of the line is 5.

The point slope form of the line is y=5x+6.

Step-by-step explanation:

We can find the slope using this formula: $\frac{y_{2} }{x_{2} } -\frac{y_{1} }{x_{1} }$