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Sphinxa [80]
3 years ago
13

At breakfast, he drinks 237 milliliters. At lunch, he drinks 300 milliliters.

Mathematics
1 answer:
Lostsunrise [7]3 years ago
5 0

Answer:

  •  Total\ amount\ of\ water\approx720\ ml (Estimation)
  • Actual\ amount\ of\ water=714\ ml

Step-by-step explanation:

<h3> The complete exercise is:</h3><h3> "At breakfast, he drinks 237 milliliters. At lunch, he drinks 300 milliliters. At dinner, he drinks 177 milliliters. Estimate the total amount of water Rogelio drinks. Then, find the actual amount of water he drinks at all three meals."</h3>

In order to estimate the total amount of water Rogelio drinks at all three meals, you need to follow these steps:

1. Round 237 milliliters and 177 milliliters to the nearest Tens place.

If the digit in the Ones place is less than 5, you must round down.

If the digit in the Ones place is greater than or equal to 5, you must round up.

Then:

237\ ml\approx240\ ml\\\\177\ ml\approx180\ ml

2. Add 240 milliliters, 300 milliliters and 180 milliliters:

Total\ amount\ of\ water\approx240\ ml+300\ ml+180\ ml\approx720\ ml

In order to  find the actual amount of water Rogelio drinks at all three meals, just add 237 milliliters, 300 milliliters and 177 milliliters. This is:

Actual\ amount\ of\ water=237\ ml+300\ ml+177\ ml=714\ ml

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ahrayia [7]

Answer:

A) Two populations: American men and American women, as it estimated from the broad of the survey.

B) The proportion of men that sometimes do not drive safely while talking or texting on cell phone is 32%, and the proportion of women that sometimes do not drive safely while talking or texting on cell phone is 25%.

C) There is enough evidence to support the claim that the proportion of men and women who used their cell phone in an emergency differ significantly (P-value=0.014).

Step-by-step explanation:

A. We have two populations: American men and American women. This are the populations from which we want to infere the difference of means.

B. The estimation of the proportion is already shown in the question:

The proportion of men that sometimes do not drive safely while talking or texting on cell phone is 32%, and the proportion of women that sometimes do not drive safely while talking or texting on cell phone is 25%.

These are unbiased estimators of the populations proportions.

C. This is a hypothesis test for the difference between proportions.

The claim is that the proportion of men and women who used their cell phone in an emergency differ significantly.

Then, the null and alternative hypothesis are:

H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0

The significance level is 0.05.

The sample 1 (men), of size n1=643 has a proportion of p1=0.71.

The sample 2 (women), of size n2=643 has a proportion of p2=0.77.

 

The difference between proportions is (p1-p2)=-0.06.

p_d=p_1-p_2=0.71-0.77=-0.06

The pooled proportion, needed to calculate the standard error, is:

p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{457+495.11}{643+643}=\dfrac{952}{1286}=0.7403

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

s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.7403*0.2597}{643}+\dfrac{0.7403*0.2597}{643}}\\\\\\s_{p1-p2}=\sqrt{0.0003+0.0003}=\sqrt{0.0006}=0.0245

Then, we can calculate the z-statistic as:

z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.06-0}{0.0245}=\dfrac{-0.06}{0.0245}=-2.45

This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):

P-value=2\cdot P(z

As the P-value (0.014) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the proportion of men and women who used their cell phone in an emergency differ significantly.

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