77/99 as a fraction or mixed number in simplest form

The manager at a sports radio station will be covering several football games over the weekend. She knows that most of her liste

Paraphin [41]

Complete Question:

The manager at a sports radio station will be covering several football games over the weekend. She knows that most of her listeners are at least 22 years old and wants to know what age group she should gear her advertisements to for the games. She takes a random sample of 46 listeners from age 22-39 and 57 listeners who are 40 and older and asks them if they are likely to tune in to football games. The "yes" responses are recorded in the file attached below.

1. At the 0.05 level of significance, is there a significant difference in the proportion of listeners based on age?

2. Is there evidence to suggest that there is a significant difference in the proportion of listeners based on age?

Answer:

1) There is no significant difference in the proportion of listeners based on age

2) No, there is no evidence

Step-by-step explanation:

Sample size of group 1, $n_1 = 46$

Sample size of group 2, $n_2 = 57$

Number of Yes in group 1, $X_1 = 32$

Number of Yes in group 2, $X_2 = 47$

Proportion of Yes in group 1:

$\hat{p_1} = \frac{X_1}{n_1} \\\hat{p_1} = \frac{32}{46}\\\hat{p_1} = 0.6957$

Proportion of Yes in group 2:

$\hat{p_2} = \frac{X_2}{n_2} \\\hat{p_2} = \frac{47}{57}\\\hat{p_2} = 0.8246$

Null Hypothesis, $H_0: p_1 = p_2$

Alternate Hypothesis, $H_a: p_1 \neq p_2$

$\hat{p} = \frac{X_1 + X_2}{n_1 + n_2} \\\\\hat{p} = \frac{ 32+47}{46+57} \\\\\hat{p}= 0.767$

Significance level,

Calculate the test statistic

$z = (\hat{p_1} - \hat{p_2})/\sqrt{(\hat{p} * (1-\hat{p}) * (\frac{1}{N_1} + \frac{1}{N_2})}\\\\z = (0.6957-0.8246)/ \sqrt{(0.767*(1-0.767)*(1/46 + 1/57))}\\\\z = -1.54$

Get the P-value from the probability distribution table:

At z = -1.54, P-value = 0.1236

Since (P-value = 0.1236) > (α = 0.05), we will accept the null hypothesis. This means that there is no evidence to suggest that there is difference in the proportion of listeners based on age.

7 0

3 years ago

Oil consumption is increasing at a rate of 1.8% per year. by what factor will oil consumption increase inn 6 years? Use the appr

Vesna [10]

$\frac{70}{1,8} \approx 38.8 \ \ \ \ \ \rightarrow \ the \ amount \ of \ time \ to \ double \ the \ consumption \\ \\
38,8 - 100\% \\ 6 - x \\
38,8 x = 600\% \\x \approx 15.5\% \\ \\
In \ six \ years \ oil \ consumption \ will \ increase \ by \ approximately \ 15.5\%$

6 0

3 years ago

Read 2 more answers

A plumbers plastic pipe is 4 m long, has an inside diameter of 4.0 cm and an outside diameter of 5.0cm. What is the volume of th

SCORPION-xisa [38]

Answer: $V=0.0028278\ m^3$

Step-by-step explanation:

Given

Length of the pipe $l=4\ m$

Inside diameter of the pipe $d_i=4\ cm$

Outside diameter of the pipe $d_o=5\ cm$

Volume of the pipe

$\Rightarrow V=\dfrac{\pi }{4}[d_o^2-d_i^2]\\\\\text{Insert the values}\\\\\Rightarrow V=\dfrac{\pi}{4}[5^2-4^2]\times 10^{-4}\times 4\\\\\Rightarrow V=28.278\times 10^{-4}\ m^3\\\\\Rightarrow V=0.0028278\ m^3$

5 0

3 years ago

Can someone please help me with math.

iragen [17]

Answer:

Answer C 2,799.159

Step-by-step explanation:

$v=\pi r^{2} h$

5 0

3 years ago

What is the a-value of the function, then determine if the graph opening up or down f(x)=−5(x+7)2+6?

Kay [80]

We know that
the equation of the vertical parabola in the vertex form is
y=a(x-h)²+k
where
(h,k) is the vertex of the parabola
if a> 0 then
the parabola opens upwards

if a< 0
then the parabola open downwards

in this problem we have
f(x)=−5(x+7)²+6
a=-5
so
a< 0 -------> the parabola open downwards

the vertex is the point (-7,6) is a maximum

the answer is the option
a = -5, opens down

see the attached figure

6 0

3 years ago

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