Is 0.641 x 10^3 correct scientific notation

It is thought that the front cover and the nature of the first question on mail surveys influence the response rate. An article

denis-greek [22]

Answer:

The null and alternative hypothesis are:

$H_0: \pi_1=\pi_2\\\\H_a:\pi_1\neq \pi_2$

Test statistic z = -0.29

P-value = 0.7709

Fail to reject H0. The data does not suggest that the front cover and nature of the first question on mail surveys influence the response rate.

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that the return rate is different for the Plain cover and the Skydiver cover.

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 0.1.

The sample 1 (plain cover), of size n1=209 has a proportion of p1=0.493.

$p_1=X_1/n_1=103/209=0.493$

The sample 2 (skydiver cover), of size n2=215 has a proportion of p2=0.507.

$p_2=X_2/n_2=109/215=0.507$

The difference between proportions is (p1-p2)=-0.014.

$p_d=p_1-p_2=0.493-0.507=-0.014$

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

$p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{103+109}{209+215}=\dfrac{212}{424}=0.5$

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

$s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.5*0.5}{209}+\dfrac{0.5*0.5}{215}}\\\\\\s_{p1-p2}=\sqrt{0.001196+0.001163}=\sqrt{0.002359}=0.049$

Then, we can calculate the z-statistic as:

$z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.014-0}{0.049}=\dfrac{-0.014}{0.049}=-0.29$

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

$\text{P-value}=2\cdot P(z$

As the P-value (0.771) is bigger than the significance level (0.1), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the return rate is different for the Plain cover and the Skydiver cover.

8 0

3 years ago

in a three digit number, the sum of the digits in the units and the hundreds positions is equal to the number of tens. One more

Nastasia [14]

964 is correct i did the math rn

3 0

2 years ago

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A local rectangular shaped pool used by lap swimmers has dimensions 25 yd by 30 yd and is 5.1 feet deep. Find the cost for filli

Lelu [443]

Answer:

the cost of filling the pool is $386.3

Step-by-step explanation:

Given;

dimension of the rectangular pool, = 25 yd by 30 yd by 5.1 ft

covert the given dimensions to feet;

1 yd = 3 ft

25 yd = 25 x 3 ft = 75 ft

30 yd = 30 x 3 ft = 90 ft

The volume of the rectangular pool in cubic feet (ft³);

Volume = 75 ft x 90 ft x 5.1 ft

Volume = 34,425 ft³

Convert the volume to gallons;

1 ft³ = 7.481 gallons

10,125 ft³ = 34,425 x 7.481 gallons

= 257,533.425 gallons

The cost per a 1000 gallons is $1.50, then cost of the 257,533.425 gallons is calculated as;

$cost = \frac{\$ 1.50}{1000 \ gallons} \times 257,533.425 \ gallons = \$ 386.3$

Therefore, the cost of filling the pool is $386.3

6 0

3 years ago

11. f(x) = x + 3, g(x) = -x + 2. Find (f + g)(x)

NeTakaya

Answer:

(f + g)(x) = 5

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Terms/Coefficients
Functions
Function Notation

Step-by-step explanation:

Step 1: Define

Identify

f(x) = x + 3

g(x) = -x + 2

(f + g)(x) is f(x) + g(x)

Step 2: Find

Substitute in function values: (f + g)(x) = x + 3 - x + 2
[Subtraction] Combine like terms (x): (f + g)(x) = 3 + 2
Add: (f + g)(x) = 5

5 0

3 years ago

What is 4y+3x-10y+7x

Rus_ich [418]

10x-6y
You have to add the like terms.

3 0

4 years ago

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