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A professor wishes to discover if seniors skip more classes than freshmen. Suppose he knows that freshmen skip 2% of their class

KIM [24]

Answer:

We conclude that seniors skip more than 2% of their classes at 0.01 level of significance.

Step-by-step explanation:

We are given that a professor wishes to discover if seniors skip more classes than freshmen. Suppose he knows that freshmen skip 2% of their classes.

He randomly samples a group of seniors and out of 2521 classes, the group skipped 77.

Let p = percentage of seniors who skip their classes.

So, Null Hypothesis, $H_0$ : p $\leq$ 2% {means that seniors skip less than or equal to 2% of their classes}

Alternate Hypothesis, $H_A$ : p > 2% {means that seniors skip more than 2% of their classes}

The test statistics that will be used here is One-sample z proportion statistics;

T.S. = $\frac{\hat p-p}{{\sqrt{\frac{\hat p(1-\hat p)}{n} } } } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of seniors who skipped their classes = $\frac{77}{2521}$

n = sample of classes = 2521

So, test statistics = $\frac{\frac{77}{2521} -0.02}{{\sqrt{\frac{\frac{77}{2521}(1-\frac{77}{2521})}{2521} } } } }$

= 3.08

The value of the test statistics is 3.08.

Now at 0.01 significance level, the z table gives critical value of 2.3263 for right-tailed test. Since our test statistics is more than the critical value of z as 2.3263 < 3.08, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that seniors skip more than 2% of their classes.

6 0

3 years ago

Line segment MN has endpoints M(4,-5) and N(-3,1). Find MN.

pshichka [43]

9.2195444572928873100022742817628. or square root of 85

8 0

2 years ago

Can someone please!!! Help me

timurjin [86]

The answer to this question is true

7 0

2 years ago

The graph shows the dilation of ΔABC with the origin as its center. Which rule describes this transformation? A) (x, y) → (2x, 2

podryga [215]

Note: Since, you have not added the graph. So, I will give you a general overview of the concept of dilation, the understanding of which will make you clear your concept.

Step-by-step explanation:

We know that a dilation is the kind of transformation which produces an image which has the same shape as the original object, but having a different size.

Here are some key factors regarding dilation:

Enlargement occurs when a dilation does create a larger image.

Reduction occurs when a dilation does create a smaller image.

A dilation shrinks or stretches the original object.
If the scale factor > 1, the image will be a stretch (enlargement)
If the scale factor is between 0 and 1, the image will be shrunk (reduction)
If the scale factor = 1, the original object and the image will be congruent

Here is the impact of dilation when (x, y) → (2x, 2y):

Dilation with scale factor 2, will have the rule as (x, y) → (2x, 2y). The image will be a stretch (enlargement) as the scale factor > 1.
The location of the new coordinates of the image can be obtained by multiplying the coordinates of the original figure by 2.

For example, the coordinates of the image of a point A(4, 8) will be A'(2×4, 2×8) or A'(8, 16) after the dilation of scale 2 at the origin.

Here is the impact of dilation when (x, y) → (0.5x, 0.5y):

Dilation with scale factor 0.5, will have the rule as (x, y) → (0.5x, 0.5y). The image will be shrunk (reduction) as the scale factor < 1.
The location of the new coordinates of the image can be obtained by multiplying the coordinates of the original figure by 0.5.

For example, the coordinates of the image of a point A(4, 8) will be A'(0.5×4, 0.5×8) or A'(2, 4) after the dilation of scale 0.5 at the origin.

Keywords: dilation, transformation, enlargement, reduction

Learn more about dilation from brainly.com/question/13846651

#learnwithBrainly

8 0

3 years ago

If s= the number of stamps that sara has, which mathematical sentence expresses the information?

Monica [59]

S*x!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

7 0

3 years ago