Question 888626: I am having issues finding the answer to this statistics problem. Please help me work this out! Thank you!
According to the College Research Center, the proportion of college students who use only a cellular telephone (no land line) is 76%. Considering this, your instructor surveyed his students to see how they compared.
From 359 college students surveyed, he found that 262 of them only used a cellular telephone. Consequently, your instructor claims that his college students are different from other college students.
Test your instructor's claim at a level of significance of 10% using the P-Value Method:
The following parts break down the four steps of the P-Value Method, which you will use for the hypothesis test in this problem:
A) State the Hypotheses
B) Determine the Test Statistic.
C) Determine the P-Value.
D) State the conclusion. It should be in terms of the problem (give me more than just Reject Ho or Do Not Reject Ho).
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! note that 262 / 359 = 0.729805014 or 73%
now 0.76 of 359 = 272.84 or 273 (expected value) vs 262 (observed value)
now 0.24 0f 359 = 86.16 or 86 (expected value vs 97 (observed value)
A) The proportion of college students who use only a cellular telephone (no land line) is 76%.
B) Level of significance is 10% or alpha = 0.10
C) Degree of freedom is 2 -1 = 1
x = ((262 - 273)^2 / 273) + ((86 - 97)^2 / 97)
x = (-11)^2 / 273 + (-11)^2 / 97 = 0.443223443 + 1.24742268 = 1.690646123 = 1.69
our chi-square value is 1.69, now we consult the chi-square table to determine our p-value, using our degree of freedom of 1, we scan that row from left to right looking for a chi-square value greater than 1.69 and we find that value of 2.07 with a p-value of 15%
thus our p-value lies between 15% - 20%
D) This means there's a 15-20% chance that the results we observed weren't the result of a change in location (instructor's students, as opposed to the entire nation), but instead just happened by chance. Since we were looking for a chance of less than 10%, we can't say that we're sure our instructor's students are less biased towards using cell phones only - there's a small but statistically significant chance they aren't.
|
|
|
