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QveST [7]
3 years ago
14

You are testing the claim that the proportion of men who own cats is significantly different than the proportion of women who ow

n cats. You sample 80 men, and 55% own cats. You sample 100 women, and 30% own cats. Find the test statistic, rounded to two decimal places. 41.11Incorrect
Mathematics
1 answer:
otez555 [7]3 years ago
5 0

Answer:

Step-by-step explanation:

This is a test of 2 population proportions. Let 1 and 2 be the subscript for the men and women who own cats respectively. The population proportion of men and women who own cats would be p1 and p2 respectively.

p1 - p2 = difference in the proportion of men and women who own cats.

The null hypothesis is

H0 : p1 = p2

p1 - p2 = 0

The alternative hypothesis is

Ha : p1 ≠ p2

p1 - p2 ≠ 0

it is a two tailed test

Sample proportion = x/n

Where

x represents number of success

n represents number of samples

For men

n1 = 80

p1 = 55/100 = 0.55

x1 = p1n1 = 0.55 × 80 = 44

For women,

n2 = 100

p2 = 30/100 = 0.3

x2 = p2n2 = 0.3 × 100 = 30

The pooled proportion, pc is

pc = (x1 + x2)/(n1 + n2)

pc = (44 + 30)/(80 + 100) = 0.41

1 - pc = 1 - 0.41 = 0.59

z = (p1 - p2)/√pc(1 - pc)(1/n1 + 1/n2)

z = (0.55 - 0.3)/√(0.41)(0.59)(1/80 + 1/100) = 3.39

Test statistic = 3.39

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This statement is false

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In a jar of coins, the ratio of nickels to dimes is 2:7. If the jar contains 350 nickels, how many dimes are there? A) 175 B) 35
Dvinal [7]
No nickles = 2x and that of dimes = 7x so 2x = 350 get x and the no of dimes
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3 0
3 years ago
Read 2 more answers
A pizza pan is removed at 9:00 PM from an oven whose temperature is fixed at 450°F into a room that is a constant 70°F. After 5​
gladu [14]

Answer:

A) It will get to a temperature of 125°F at 9:19 PM

B) It will get to a temperature of 150°F at 9:16 PM

C) as time passes temperature approaches the initial temperature of 450°F

Step-by-step explanation:

We are given;

Initial temperature; T_i = 450°F

Room temperature; T_r = 70°F

From Newton's law of cooling, temperature after time (t) is given as;

T(t) = T_r + (T_i - T_r)e^(-kt)

Where k is cooling rate and t is time after the initial temperature.

Now, we are told that After 5​ minutes, the temperature is 300°F.

Thus;

300 = 70 + (450 - 70)e^(-5k)

300 - 70 = 380e^(-5k)

230/380 = e^(-5k)

e^(-5k) = 0.6053

-5k = In 0.6053

-5k = -0.502

k = 0.502/5

k = 0.1004 /min

A) Thus, at temperature of 125°F, we can find the time from;

125 = 70 + (450 - 70)e^(-0.1004t)

125 - 70 = 380e^(-0.1004t)

55/380 = e^(-0.1004t)

In (55/380) = -0.1004t

-0.1004t = -1.9328

t = 1.9328/0.1018

t ≈ 19 minutes

Thus, it will get to a temperature of 125°F at 9:19 PM

B) Thus, at temperature of 150°F, we can find the time from;

150 = 70 + (450 - 70)e^(-0.1004t)

150 - 70 = 380e^(-0.1004t)

80/380 = e^(-0.1004t)

In (80/380) = -0.1004t

-0.1004t = -1.5581

t = 1.5581/0.1004

t ≈ 16 minutes.

Thus, it will get to a temperature of 150°F at 9:16 PM

C) As time passes which means as it approaches to infinity, it means that e^(-kt) gets to 1.

Thus,we have;

T(t) = T_r + (T_i - T_r)

T_r will cancel out to give;

T(t) = T_i

Thus, as time passes temperature approaches the initial temperature of 450°F

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