Question

Students at the Akademia Podlaka conducted an experiment to determine whether the Belgium-minted Euro coin was equally likely to land heads up or tails up. Coins were spun on a smooth surface, and in 200 spins, 150 landed with the heads side up. Should the students interpret this result as convincing evidence that the proportion of the time the coin would land heads up is not 0.5? Test the relevant hypotheses using α = 0.01. Would your conclusion be different if a significance level of 0.05 had been used? (For z give the answer to two decimal places. For P give the answer to four decimal places.)z = P = For α = 0.01
There is  ---Select--- enough not enough evidence to suggest that the proportion of the time that the Belgium Euro coin would land with its head side up is not 0.5.
For α = 0.05
There is  ---Select--- enough not enough evidence to suggest that the proportion of the time that the Belgium Euro coin would land with its head s

Answer 1

Answer:

Given that,

Students at the Akademia Podlaka conducted an experiment to determine whether the Belgium-minted Euro coin was equally likely to land heads up or tails up.

Coins were spun on a smooth surface, and in 200 spins, 150 landed with the heads side up.

Test the relevant hypotheses using α = 0.01

Should the students interpret this result as convincing evidence that the proportion of the time the coin would land heads up is not 0.5?

Would your conclusion be different if a significance level of 0.05 had been used:

We have the following information:

Number of spins=200

The number of times heads obtained 150.

=0.5 proportion of the time the coin would land heads up.

We have to test the relevant hypothesis using =0.05, and then we need to verify our conclusion is different if a significance level of =0.05.

The null and alternative hypotheses are defined as follows:

The proportion of the time that the coin would land heads up is 0.5.

The proportion of the time that the coin would land heads up is not 0.5.

Assumptions:

This test requires a random sample and a large sample size.

The given sample was a random sample; the population size is much larger than the sample size.

And the sample size was n=200.

np=200(0.5)

=100

10

nq=200(1-0.5)

=200(0.5)

=100

10

The sample proportion of heads is obtained as follows:

=0.75

The value of the test statistic is calculated as follows:

=7.070135

z=7.07 (Approximately)

Therefore, the value of the test statistic is (z)=7.07.

The p-value:

Twice the area under the Z curve to the right of 7.07 is 0.00001 so, the p-value is 0.00001.

At the significance level 0.01, we reject because the p-value of 0.00001 is less than the significance level of 0.01.

At the significance level 0.05, we reject because the p-value of 0.00001 is less than the significance level of 0.05.

The data provide convincing evidence that the proportion of the time the coin would land heads up of accidents involving teenage drivers is different from 0.5.

The conclusion is changed if there is a change in level of significance from 0.01 to 0.05.