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kupik [55]
3 years ago
9

Principal clements wants to buy a pencil for each of the 57 fourth graders in her school. The pencils come in packages of 6. How

many packages does principal clements need to buy?
Mathematics
1 answer:
Scrat [10]3 years ago
8 0

Principal clements needs to buy 10 packages

<em><u>Solution:</u></em>

Given that, Principal clements wants to buy a pencil for each of the 57 fourth graders in her school

The pencils come in packages of 6

Therefore,

Total number of students = 57

<em><u>Thus, divide 57 by 6 to get the number of packages clements need to buy</u></em>

\text{Number of packages } = \frac{\text{total number of students }}{6}<em><u></u></em>

<em><u>Substituting the given values we get,</u></em>

\text{Number of packages } = \frac{57}{6} \\\\\text{Number of packages }= 9.5 \approx 10

Thus principal clements needs to buy 10 packages

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where μ1: mean calorie estimation for the cheesecake group and μ2: mean calorie estimation for the organic salad group.

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<em>The question is incomplete:</em>

<em>"Suppose that the study was based on a sample of 20 people who thought about the cheesecake first and 20 people who thought about the organic fruit salad first, and the standard deviation of the number of calories in the cheeseburger was 128 for the people who thought about the cheesecake first and 140 for the people who thought about the organic fruit salad first.</em>

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This is a hypothesis test for the difference between populations means.

The claim is that the mean estimated number of calories in the cheeseburger is lower for the people who thought about the cheesecake first than for the people who thought about the organic fruit salad first.

Then, the null and alternative hypothesis are:

H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2> 0

The significance level is 0.01.

The sample 1 (cheese cake), of size n1=20 has a mean of 780 and a standard deviation of 128.

The sample 2 (organic salad), of size n2=20 has a mean of 1041 and a standard deviation of 140.

The difference between sample means is Md=-261.

M_d=M_1-M_2=780-1041=-261

The estimated standard error of the difference between means is computed using the formula:

s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{128^2}{20}+\dfrac{140^2}{20}}\\\\\\s_{M_d}=\sqrt{819.2+980}=\sqrt{1799.2}=42.417

Then, we can calculate the t-statistic as:

t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{-261-0}{42.417}=\dfrac{-261}{42.417}=-6.153

The degrees of freedom for this test are:

df=n_1+n_2-1=20+20-2=38

This test is a left-tailed test, with 38 degrees of freedom and t=-6.153, so the P-value for this test is calculated as (using a t-table):

P-value=P(t

As the P-value (0.0000002) is smaller than the significance level (0.01), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the mean estimated number of calories in the cheeseburger is lower for the people who thought about the cheesecake first than for the people who thought about the organic fruit salad first.

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