# P-Value

Please provide step by step instructions on how to solve the following problems using actual numbers provided. Thanks

1) A student representative claims that 60% of the students favor a move to division 1. A random sample of 250 students were selected and 140 of them indicated they favored a move to division 1.

a. Perform the appropriate test of hypothesis to test the representative's claim. Use alpha=.05.

b. Write out each step in determining the p-value for the test in part one.

2) The manager of a movie rental store was interested in examining the relationship between the weekly take-home pay for a family and the amount that family spends weekly on recreational activites. The following output was generated using Minitab:

Covariances

takehome 4413.84

recreation 2419.64 1364.29

Let 2=weekly take-home pay and y=amount spent weekly on recreational activities

a. identify s of x squared (=4413.84)

b. s of xy (=1364.29)

c. s of y squared (=2419.64)

d. calculate the correlation between weekly take-home pay and amount spent weeky on recreational activities.

e. Interpret the correlation coefficient found in part d.

https://brainmass.com/statistics/hypothesis-testing/p-value-7088

#### Solution Preview

1) Solution. Let us define two hypothesis.

<br> H0: p=0.6; H1:p is not equal to 0.6

<br>where p is the probability that the students favor a move to division 1.

<br>

<br> We define the following random variables Xi, i=1,2,...,250, where

<br>Xi=1 if the ith people favor a move to division 1; otherwise Xi=0, i=1,2,...,250.

<br>

<br>If the hypothesis H0 is true, then by the laws of large numbers in probability we know that X*=(X1+X2+...+X250)/250 should approximately follow normal distribution ...

#### Solution Summary

The solution addresses - 1) A student representative claims that 60% of the students favor a move to division 1. A random sample of 250 students were selected and 140 of them indicated they favored a move to division 1.

a. Perform the appropriate test of hypothesis to test the representative's claim. Use alpha=.05.

b. Write out each step in determining the p-value for the test in part one.

2) The manager of a movie rental store was interested in examining the relationship between the weekly take-home pay for a family and the amount that family spends weekly on recreational activites. The following output was generated using Minitab:

Covariances

takehome 4413.84

recreation 2419.64 1364.29

Let 2=weekly take-home pay and y=amount spent weekly on recreational activities

a. identify s of x squared (=4413.84)

b. s of xy (=1364.29)

c. s of y squared (=2419.64)

d. calculate the correlation between weekly take-home pay and amount spent weeky on recreational activities.

e. Interpret the correlation coefficient found in part d.