Null Hypothesis, significance level, help

[Calculator14]

Homework Statement

You wish to test whether or not a coin is fair, so you toss it 400 times and obtain 225 heads. Test the null hypothesis that the coin is fair and balanced against the alternative that it is not. Use the 5% significance level.
a.) Identify(using symbols) the null and alternative hypotheses.
b.) Is this a right tailed, left tailed or two-tailed test?
c.) Identify the appropriate distribution; give its mean and standard deviation.
d.) State the formula for the test statistic; substitute the specific values, then calculate the resultant.
e.) Determine the P-value.
f.) What is your decision?
g.) State your conclusion.

Homework Equations

(work shown below)

The Attempt at a Solution

a.) Identify the null and alternative hypotheses.
Ho: The coin is fair.
H1: The coin is not fair.

b.) Is this a right tailed, left tailed or two-tailed test?
Two tailed test because it may be higher or lower.

c.) Identify the appropriate distribution; give its mean and standard deviation.
Normal distribution
p=.5
σ= (.5(1-.5))^1/2 / (400)^1/2 = 0.025

d.) State the formula for the test statistic; substitute the specific values, then calculate the resultant.
Formula for test statistic: - p / σ
= 225/400 = 0.5625
0.5625 - .5 / 0.025 = 2.5

e.)Determine the P-value.
P= (1-.9938)2 = 0.0124

f.) What is your decision?
P Value(0.0124) is less than the significance level (0.05) so we reject the null hypothesis.

g.)State your conclusion.
The coin is not fair.

 

[member38644]

The probability of obtaining 225 heads out of 400 tosses is significantly lower than the significance level of 5%. Therefore, we reject the null hypothesis that the coin is fair and conclude that the coin is not balanced.