What is the square root of -169

Last year it was found that on average it took students 20 minutes to fill out the forms required for graduation. This year the

Darina [25.2K]

Answer:

$t=\frac{18.5-20}{\frac{5.2}{\sqrt{22}}}=-1.35$

$p_v =P(t_{21}$

If we compare the p value and a significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we FAIL to reject the null hypothesis, and the actual true mean for the time is not significantly less than 20 minutes at 5% of significance.

Step-by-step explanation:

Data given and notation

$\bar X=18.5$ represent the sample mean

$s=5.2$ represent the standard deviation for the sample

$n=22$ sample size

$\mu_o =20$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses to be tested

We need to conduct a hypothesis in order to determine if the mean for the new forms take less time to complete than the older forms, the system of hypothesis would be:

Null hypothesis: $\mu \geq 20$

Alternative hypothesis: $\mu < 20$

Compute the test statistic

We don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

We can replace in formula (1) the info given like this:

$t=\frac{18.5-20}{\frac{5.2}{\sqrt{22}}}=-1.35$

Now we need to find the degrees of freedom for the t distirbution given by:

$df=n-1=22-1=21$

What do you conclude?

Compute the p-value

Since is a one left tailed test the p value would be:

$p_v =P(t_{21}$

If we compare the p value and a significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we FAIL to reject the null hypothesis, and the actual true mean for the time is not significantly less than 20 minutes at 5% of significance.

7 0

3 years ago

The base and height of the triangle of the triangle at the right are multiplied by 4. Describe the change in the area. Justify y

dimulka [17.4K]

5 meters and 6 meters? Where the heck did you get 5 and 6 from is there like some sort of magic going on? Is this Disney!? IS the height 5 m and the base is 6 m or what because I can't help you with Disney's magic stuff. IS THERE LIKE ALL OF A SUDDEN 2 triangles?
wow.

3 0

3 years ago

Four interior angles of a pentagon measure 88°, 118°, 132°, and 100°. What is the measure of the fifth interior angle?

bearhunter [10]

Answer:

102 deg

Step-by-step explanation:

The sum of the interior angles of a n-gon

are equal to ( n-2)*180

for a pentagon ( 5-2)(180) = 540

88+118+132+100 + x = 540 x= 102 deg

8 0

2 years ago

A coin is tossed and a die is rolled simultaneously. What is the probability of getting a tail and a number less than 3?

Reil [10]

Answer: 1/6

Step-by-step explanation:

Probability of getting heads or tail is:

P (H) = P(T) = 1/2

The probability of getting any number on the die is:

P (1) = P (2) = P(3) = P (4) = P (5) = P (6) = 1/6

The probability of getting a tail on the coin and a number less than 3 on the die is:

$P($Tails and a number less than 3$)=P($Tails$) \times P$(A number less than 3)$$\begin{aligned}&=\frac{1}{2} \times[P(1)+P(2)] \\&=\frac{1}{2} \times\left[\frac{1}{6}+\frac{1}{6}\right] \\&=\frac{1}{6}\end{aligned}$$$

Therefore the required of getting tails and a number less than 3 is 1/6

7 0

2 years ago

The sum of three consecutive even integers is 168. Define an appropriate variable and write an equation that represents the stat

bulgar [2K]

Answer:

a, a + 1, a + 2

55, 56. 57

Step-by-step explanation:

Let the integers be :

a, a + 1, a + 2 (consecutive integers)

Hence, sum of the integers equals 168

a + (a + 1) + (a + 2) = 168

a + a + 1 + a + 2 = 168

3a + 3 = 168

3a = 168 - 3

3a = 165

a = 165 / 3

a = 55

first integer, a = 55

Second, a +1 = 56

Third, a + 2 = 57

3 0

3 years ago