Solve for the compound inequality 6b

At Western University the historical mean of scholarship examination scores for freshman applications is 900. A historical popul

vampirchik [111]

Answer:

a) Null Hypothesis: $\mu =900$

Alternative hypothesis: $\mu \neq 900$

b) The 95% confidence interval would be given by (910.05;959.95)

c) Since we confidence interval not ocntains the value of 900 we fail to reject the null hypothesis that the true mean is 900.

d) $z=\frac{935 -900}{\frac{180}{\sqrt{200}}}=2.750$

Since is a bilateral test the p value is given by:

$p_v =2*P(Z>2.750)=0.0059$

Step-by-step explanation:

a. State the hypotheses.

On this case we want to check the following system of hypothesis:

Null Hypothesis: $\mu =900$

Alternative hypothesis: $\mu \neq 900$

b. What is the 95% confidence interval estimate of the population mean examination score if a sample of 200 applications provided a sample mean x¯¯¯= 935?

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=935$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma=180$ represent the population standard deviation

n=200 represent the sample size

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

In order to calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=3278.222$

The sample deviation calculated $s=97.054$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

Now we have everything in order to replace into formula (1):

$935-1.96\frac{180}{\sqrt{200}}=910.05$

$935+1.96\frac{180}{\sqrt{200}}=959.95$

So on this case the 95% confidence interval would be given by (910.05;959.95)

c. Use the confidence interval to conduct a hypothesis test. Using α= .05, what is your conclusion?

Since we confidence interval not ocntains the value of 900 we fail to reject the null hypothesis that the true mean is 900.

d. What is the p-value?

The statistic is given by:

$z=\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

If we replace we got:

$z=\frac{935 -900}{\frac{180}{\sqrt{200}}}=2.750$

Since is a bilateral test the p value is given by:

$p_v =2*P(Z>2.750)=0.0059$

So then since the p value is less than the significance we can reject the null hypothesis at 5% of significance.

8 0

3 years ago

Perimeter is a measure of distance around a figure. If each side of a triangle measures 0.75 inches, what is the perimeter of th

Alexxx [7]

Perimeter = 0.75 * 3 = 2.25 inches

3 0

3 years ago

Is a triangle with the side lengths 15, 36, and 39 a right triangle?

Alex73 [517]

Answer:

yes

Step-by-step explanation:

8 0

2 years ago

4. Tyson and his friends go ice skating. Tyson must pay an initial fee of $18.30 plus $4.80 per hour.

hjlf

Answer:

equation: c = 4.80h + 18.30, cost for four hours: (4, 37.5)

Step-by-step explanation:

the equation is c = 4.80h + 18.30 because 18.30, the initial cost, is the y-intercept and because each hour costs $4.80. the cost for four hours would be (4, 37.5) because it costs $37.5 to skate for four hours.

7 0

2 years ago

1/4 inch cubes were used to fill a prism. The dimensions of the prism are 1.5 inches x 1 inch x 3.75 inches. How many 1/4 inch c

iren2701 [21]

Answer:

B) 360 cubes

Step-by-step explanation:

We can start by finding how many cubes fit into the length of the prism (1.5 in) which is 6 cubes for 1.5 in/ 0.25 in = 6.

Then we can find the number of cubes to fit the width of the prism (1 in) which is 4 cubes for 1 in/ 0.25 in = 4.

Finally we find that 15 cubes fit the height (3.75 in) for 3.75 in/ 0.25 in = 15 cubes.

Multiplying the together, we get 6*4*15=360 or B

4 0

2 years ago

Solve for the compound inequality 6b < 42 or 4b + 12 > 8.