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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.

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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.

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 provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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