Question

1) Compared the lengths of the different Harry Potter movies and the Star Wars movies. Each series has 8 main movies that I will compare the lengths of. I will be testing my hypothesis that Harry Potter movies are longer than Star Wars movies.

The Harry Potter lengths in minutes are: 152, 161, 142, 157, 139, 153, 146, 130

The Star Wars lengths in minutes are: 133, 142, 140, 121, 124, 131, 138, 152

also:

2) The proportion of adults in Tennessee who are gamers is more than the proportion of adults in New York who are movie go-ers. In two independent polls, you may find that 69 out of 340 California residents are gamers and 59 out of 225 New York residents are movie go-ers.

Is there enough evidence to conclude that Tennessee residents game more than New York residents watch movies at the 0.8 significance level?

Answer 1

Answer)

1)

First we need to find the mean and standard deviation

Harry potter

u1 = 147.5

S1 = 10.24

N 1 = 8

Star wars

u2 = 135.125

s2 = 10.0632

N2 = 8

As the population s.d is unknown we can use t distribution to conduct the test

Null hypothesis Ho : u1 = u2

Alternate hypothesis Ha : u1>u2

Test statistics t = (u1-u2)/standard error

Standard error = √{(s1^2/n1)+(s2^2/n2)}

After substitution

Test statistics t = 2.438

Degrees of freedom is given by smaller of n1-1, n2-1

So here df is 7

For df 7 and test statistics 2.438

P-value from t distribution is = 0.022445

As the obtained P-Value is less than 0.05

We reject the null hypothesis

(Note : u have not mentioned the significance level, i am assuming it to be 0.05, if p-value is greater than the given significance level then we fail to reject the null hypothesis)

As we have rejected the null hypothesis

We have enough evidence to support the claim that, u1>u2