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Oksanka [162]
3 years ago
5

1. If the ratio of the ages of Kissi and Esinam is 3:5 and that of Esinam and Lariba is 3:5 and

Mathematics
1 answer:
zloy xaker [14]3 years ago
4 0

Answer:

1) 48 years.

2) Question incorrect.

11 isn't a factor of 64, and 368 isn't a multiple of 64. 11 also isn't a factor of 368, hence, it would be impossible to find the unknown second number with all of these false information in the question.

Step-by-step explanation:

Let the ages of Kissi, Esinam and Lariba be x, y and z respectively.

Ratio of the ages of Kissi and Esinam is 3:5

x:y = 3:5

(x/y) = (3/5)

5x = 3y

x = (3y/5) (eqn 1)

Ratio of the ages of Esinam and Lariba is 3:5

y:z = 3:5

(y/z) = (3/5)

5y = 3z

z = (5y/3) (eqn 2)

The sum of their 3 ages is 147

x + y + z = 147 (eqn 3)

Substituting the values of x and z from eqn 1 and 2 into eqn 3, we have

(3y/5) + y + (5y/3) = 147

(49y/15) = 147

y = (147×15/49) = 45.

x = (3y/5) = (3×45/5) = 27

z = (5y/3) = (5×45/3) = 75

The ages of Kissi, Esinam and Lariba are then 27, 45 and 75 respectively.

The difference in the ages of the oldest amf the youngest is thus, 75 - 27 = 48 years.

2) This question seems to be faulty and incorrect as 11 isn't a factor of 64, and 368 isn't a multiple of 64. 11 also isn't a factor of 368, hence, it would be impossible to find the unknown second number with all of these false information in the question.

Hope this Helps!!!

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1. H0: P1 = P2

2. Ha: P1 ≠ P2

3. pooled proportion p = 0.542

4. P-value = 0.0171

5. The null hypothesis failed to be rejected.

At a signficance level of 0.01, there is not enough evidence to support the claim that there is significant difference between the exercise habits of Science majors and Math majors .

6. The 99% confidence interval for the difference between proportions is (-0.012, 0.335).

Step-by-step explanation:

We should perform a hypothesis test on the difference of proportions.

As we want to test if there is significant difference, the hypothesis are:

Null hypothesis: there is no significant difference between the proportions (p1-p2 = 0).

Alternative hypothesis: there is significant difference between the proportions (p1-p2 ≠ 0).

The sample 1 (science), of size n1=135 has a proportion of p1=0.607.

p_1=X_1/n_1=82/135=0.607

The sample 2 (math), of size n2=92 has a proportion of p2=0.446.

p_2=X_2/n_2=41/92=0.446

The difference between proportions is (p1-p2)=0.162.

p_d=p_1-p_2=0.607-0.446=0.162

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

p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{82+41}{135+92}=\dfrac{123}{227}=0.542

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{0.542*0.458}{135}+\dfrac{0.542*0.458}{92}}\\\\\\s_{p1-p2}=\sqrt{0.001839+0.002698}=\sqrt{0.004537}=0.067

Then, we can calculate the z-statistic as:

z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.162-0}{0.067}=\dfrac{0.162}{0.067}=2.4014

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

\text{P-value}=2\cdot P(z>2.4014)=0.0171

As the P-value (0.0171) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

At a signficance level of 0.01, there is not enough evidence to support the claim that there is significant difference between the exercise habits of Science majors and Math majors .

We want to calculate the bounds of a 99% confidence interval of the difference between proportions.

For a 99% CI, the critical value for z is z=2.576.

The margin of error is:

MOE=z \cdot s_{p1-p2}=2.576\cdot 0.067=0.1735

Then, the lower and upper bounds of the confidence interval are:

LL=(p_1-p_2)-z\cdot s_{p1-p2} = 0.162-0.1735=-0.012\\\\UL=(p_1-p_2)+z\cdot s_{p1-p2}= 0.162+0.1735=0.335

The 99% confidence interval for the difference between proportions is (-0.012, 0.335).

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