You and your friend skate at the same rate. You complete 5 laps in 7 minutes. How long does your friend take

Polymer composite materials have gained popularity because they have high strength to weight ratios and are relatively easy and

Brums [2.3K]

Answer:

$t=\frac{51.6-48}{\frac{1.1}{\sqrt{10}}}=10.349$

$p_v =P(t_9>10.349)=1.34x10^{-6}$

If we compare the p value and the significance level given for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we reject the null hypothesis, and the the actual mean is significantly higher than 48 MPa at 5% of significance.

Step-by-step explanation:

1) Data given and notation

$\bar X=51.6$ represent the sample mean

$s=1.1$ represent the standard deviation for the sample

$n=10$ sample size

$\mu_o =48$ represent the value that we want to test

$\alpha=0.05$ 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.

We need to conduct a hypothesis in order to determine if the mean score is higher than 48, the system of hypothesis would be:

Null hypothesis: $\mu \geq 48$

Alternative hypothesis: $\mu > 48$

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:

$t=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (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".

Calculate the statistic

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

$t=\frac{51.6-48}{\frac{1.1}{\sqrt{10}}}=10.349$

Calculate the P-value

First we find the degrees of freedom:

$df=n-1=10-1=9$

Since is a one-side upper test the p value would be:

$p_v =P(t_9>10.349)=1.34x10^{-6}$

Conclusion

If we compare the p value and the significance level given for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we reject the null hypothesis, and the the actual mean is significantly higher than 48 MPa at 5% of significance.

5 0

3 years ago

A total of 150 new recruits join an army training course. After one month, 30 have dropped out. what is the percentage decrease

Pachacha [2.7K]

So what will it be a percentage of? it will be the percentage of the original recruits, of the original 150.

for this, we need to divide the number of recruits that left over all recruits, and multiply by 100%: $\frac{30}{150} *100%= \frac{1}{5} *100%=20%$

so the number of trainees decreased by 20 %

4 0

3 years ago

Read 2 more answers

In hours Mariah can rake 3 backyards. how much of a backyard can she rake in 1hour?

Leviafan [203]

Answer: 3 or the whole backyard

Step-by-step explanation: In a hour she can rack 3 backyard. The question asked that how much of a backyard can she rake in 1 hour. She can rake the whole backyard in a hour.

7 0

3 years ago

Light in vacuum is incident on the surface of a slab of transparent material. In the vacuum the beam makes an angle of 43.8° wit

REY [17]

Answer:

Index of refraction of transparent is 1.48

Step-by-step explanation:

Snell's law states that;

n1(sinθ1) = n2(sinθ2)

Where;

n1 and n2 represent the indices of refraction for the two media, and θ1 and θ2 are the angles of incidence and refraction that the ray R makes with the normal.

In this question;

n1 = 1;

θ1 = 43.8°

θ2 = 19.3°

n2 is unknown.

Thus using Snell's law, we have;

1 x sin 43.8 = n2 x sin 19.3

n2 = (sin 43.8)/sin 19.3

n2 = 1.48

4 0

3 years ago

Dracula counter vehicles in a parking lot 4 out of 16 were motorcycles if this trend continues and he counts 8 more vehicles how

Nutka1998 [239]

Answer:

32

Step-by-step explanation:

7 0

3 years ago