3 Help this is too confusing!!!!

A recent survey of 51 students reported that the average amount of time they spent listening to music was 11.5 hours per week, w

charle [14.2K]

Answer:

90% confidence interval for the mean time per week spent listening to the radio is $11.5 \pm 1.676 \times \frac{9.2}{\sqrt{51} }$ .

Step-by-step explanation:

We are given that a recent survey of 51 students reported that the average amount of time they spent listening to music was 11.5 hours per week, with a sample standard deviation of 9.2 hours.

Firstly, the pivotal quantity for 90% confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample average amount of time spent listening to music = 11.5

s = sample standard deviation = 9.2 hours

n = sample of students = 51

$\mu$ = population mean per week spent listening to the radio

Here for constructing 90% confidence interval we have used One-sample t test statistics as we know don't about population standard deviation.

So, 90% confidence interval for the population mean, $\mu$ is ;

P(-1.676 < $t_5_0$ < 1.676) = 0.90 {As the critical value of t at 50 degree of

freedom are -1.676 & 1.676 with P = 5%}

P(-1.676 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 1.676) = 0.90

P( $-1.676 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $1.676 \times {\frac{s}{\sqrt{n} } }$ ) = 0.90

P( $\bar X-1.676 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+1.676 \times {\frac{s}{\sqrt{n} } }$ ) = 0.90

90% confidence interval for $\mu$ = [ $\bar X-1.676 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+1.676 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $11.5-1.676 \times {\frac{9.2}{\sqrt{51} } }$ , $11.5+1.676 \times {\frac{9.2}{\sqrt{51} } }$ ]

= [9.34 hours , 13.66 hours]

Therefore, 90% confidence interval for the mean time per week spent listening to the radio is [9.34 hours , 13.66 hours].

4 0

4 years ago

You are organizing a school banquet. You spend $82 on decorations. Dinner will cost $13 for each person that attends. In the equ

aniked [119]

Answer:

(69,979)

Step-by-step explanation:

In the coordinates, x is represented as 69. We can now insert this into the equation.

y = 13x + 82

Now to insert x.

y = 13(69) + 82

Now we can multiply 13 by 69.

13*69 = 897

Now fix the equation.

y = 897 + 82

Now add to get our y.

897 + 82 = 979

Substitute into the equation.

y = 979

And there is our answer. We now need to put this into the coordinates.

And we get our final answer of (69,979).

Hope this helps. Have a nice day.

3 0

3 years ago

The measured dimensions of a rectangle are 7m by 4m to the nearest whole unit. Find the minimum and maximum possible areas of th

NeTakaya

28m is the answer b/c 7x4=28

8 0

4 years ago

Line l goes through (5,-3) and is parallel to the line through (2,3) and (-5,5) find the slope of l

Alika [10]

The answer to this question is 67

6 0

3 years ago

10 POINTS!!!

Sholpan [36]

Answer:

t=1/5d

Hope this helps! :)

8 0

4 years ago