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salantis [7]
3 years ago
9

Suppose that in a random sample of 200 New York City residents 55% can name a player on the Knicks. In a random sample of 120 To

ronto residents, 70% can name a player on the Raptors. At the 5% level of significance, determine if we can conclude that the proportion of all NYC residents that can name a player on the Knicks differs from the proportion of all Toronto residents who can name a player on the Raptors. C.
a. State the null and alternative hypotheses.
b. Are all criteria for the hypothesis test satisfied?
Mathematics
1 answer:
Alenkinab [10]3 years ago
6 0

Answer:

a) The null and alternative hypothesis are:

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

b) Yes.

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that the proportion of all NYC residents that can name a player on the Knicks differs from the proportion of all Toronto residents who can name a player on the Raptors.

As the claim is that the proportions differs, the difference to reject the null hypothesis can be positive or negative. Then, this is a two-tailed test.

The null and alternative hypothesis are:

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

The conditions to met for this test are:

- The sampling method for each population is simple random sampling.

- The samples are independent.

- Each sample includes at least 10 successes and 10 failures.

\text{Failures (NY):} \, F=200*0.45=90\\\\\text{Failures (T):} \, F=120*0.3=36\\\\\text{Note: we use failures as they have the lower proportions.}

- Each population is at least 20 times as big as its sample.

This conditions are met, so all criteria for the hypothesis test is satisfied.

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Answer:

b

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
What is the product of (2x-7) and (3x + 3)?
eduard
<h3>✒️EVALUATION </h3>

==================================

\large\sf\underline{Problem:}

What is the product of (2x-7) and (3x + 3)?

  • A. 6x2 + 15x-21
  • B. 6x2 - 15x - 21
  • C. 6x2 + 15x + 21
  • D. 6x2 - 15x + 21

==================================

\large\sf\underline{Answer:}

\qquad \qquad \huge \rm Letter\:B.

*Please read and understand my solution. Don't just rely on my direct answer*

==================================

\large\sf\underline{Solution:}

Here we have the given choices:

  • A. 6x2 + 15x-21
  • B. 6x2 - 15x - 21
  • C. 6x2 + 15x + 21
  • D. 6x2 - 15x + 21

Solve this equation using the distributive property,where you multiply each term to get the number.

\begin{gathered} \rm2x - 7 = \boxed{ 6} \: \bigg| \small\boxed{\: 6 {x}^{2} } \\ \rm (7)(3) = \boxed{21} \bigg | \boxed{\: 21 x} \\ \\ \qquad \rm6x^{2}+(6x- 21x)-21 \\ \qquad \boxed{ \rm6 {x}^{2} + 15x - 21}\end{gathered}

Therefore, the correct option is letter B.

==================================

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3 0
2 years ago
Which statement is true about the measure of angle R’??
aleksley [76]

Answer:

Angle R is an Angle

Step-by-step explanation:

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4 0
3 years ago
The manufacturer of Pepsi claims that its 2-liter bottles contain, on average, no more than 250 calories. A sample of 20 2-liter
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Answer:

Yes, Sample information does indicate that a 2-liter bottle of Pepsi contains more than 250 calories  

Step-by-step explanation:  

Null Hypothesis [H0] : u < 250  

Alternate Hypothesis [H1] : u > 250 {One Tail}  

t = (x' - u) / [ sd / √n ]  

= (255 - 250) / (5.6 / √20)  

5 / (5.6 /√20)  

= 3.99  

As t ie 3.99 > t value 1.65 ie for one tail 95% confidence level. So, we reject the null hypothesis & conclude that it contains more than 250 calories.  

4 0
3 years ago
A skirt that usually sells for $40 is on sale for $30. What is the discount percent?
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10/40 * 100= 25%

25% is the answer.
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