Mathematics, 22.04.2020 01:13 lorie76

Using traditional methods, it takes 10.0 hours to receive a basic driving license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique with 12 students and observed that they had a mean of 10.2 hours with a standard deviation of 1.1. A level of significance of 0.05 will be used to determine if the technique performs differently than the traditional method. Assume the population distribution is approximately normal. Find the value of the test statistic. Round your answer to three decimal places.

Answers: 3

Show answers

Answers

Answer from: sonnyboi2305

The t-statistic is t=0.631.

Step-by-step explanation:

We have to perform an hypothesis test on the mean.

The claim is that the new method performs different from the actual method.

Then, the null and alternative hypothesis are:

$H_0: \mu=10.0\\\\H_a:\mu\neq10.0$

The significance level is 0.05.

The sample has a size n=12. The sample mean is 10.2 hours and the sample standard deviation is 1.1.

As the population standard deviation is not known, we will estimate it from the sample standard deviation and use a t-statistic.

The degrees of freedom are:

df=n-1=12-1=11

The t-statistic is:

$t=\dfrac{\bar x-\mu}{s/\sqrt{n}}=\dfrac{10.2-10.0}{1.1/\sqrt{12}}=\dfrac{0.2}{0.317}= 0.631$

The P-value of this two-tailed test, with t=0.631 and df=11, is

P-value=2P(t0.631)=0.541

The P-value is bigger than the significance level, so the effect is not significant and the null hypothesis failed to be rejected.

Answer from: ctyrector

df=n-1=12-1=11

Since is a two sided test the p value would be:

$p_v =2*P(t_{(11)}0.630)=0.5416$

Step-by-step explanation:

Data given and notation

$\bar X=10.2$ represent the sample mean

s=1.1 represent the sample standard deviation

n=12 sample size

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 check if the technique performs differently than the traditional method, the system of hypothesis would be:

Null hypothesis: $\mu = 10$

Alternative hypothesis: $\mu \neq 10.2$

If we analyze the size for the sample is < 30 and we don't know the population deviation so 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".

Calculate the statistic

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

$t=\frac{10.2-10}{\frac{1.1}{\sqrt{12}}}=0.630$

P-value

The first step is calculate the degrees of freedom, on this case:

df=n-1=12-1=11

Since is a two sided test the p value would be:

$p_v =2*P(t_{(11)}0.630)=0.5416$

Answer from: Quest

im not sure

step-by-step explanation:

Answer from: Quest

answer: asdfghjkl,mnbv

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 15:00

The lee family bought their home for $220,000 this year. the equation =220,000(1.038) v = 220 , 000 ( 1 . 038 ) x can be used to find the value, v, of their home after x years. which will be the value of the lee family's home in 5 years?

Answers: 1

Answer

Mathematics, 21.06.2019 19:30

What is the result of adding the system of equations? 2x+y=4 3x-y=6

Answers: 2

Answer

Mathematics, 21.06.2019 19:40

What is the range of the function? f(x)=-2|x+1|? a. all real numbers. b. all real numbers less than or equal to 0. c. all real numbers less than or equal to 1. d. all real numbers greater than or equal to 1

Answers: 2

Answer

Mathematics, 21.06.2019 21:00

List x1, x2, x3, x4 where xi is the midpoint endpoint of the five equal intervals used to estimate the area under the curve of f(x) between x = 0 and x = 10.

Answers: 1

Answer

You know the right answer?

Using traditional methods, it takes 10.0 hours to receive a basic driving license. A new license tra...

Questions