Please explain why you choose these answers. Thanks! 4. After a college football
ID: 3043509 • Letter: P
Question
Please explain why you choose these answers. Thanks!
4. After a college football team association conducted a survey to see if alumni were in favor o once again lost a game to their archrival, the alumni f firing the coach. A simple random sample of 100 alumni from the population of all living alumni was take Sixty-four of the alumni in the sample were in favor of firing the coach. Let p represent the proportion of all living alumni who favored firing the coach. Suppose the alumni association wished to see if the majority of alumni are in favor of firing the coach. To d this they test the hypotheses Ho: p = 0.50 versus H: p > 0.50. The alumni association wished to conduct the test at a 5% significance level. What would their decision be? Based on that decision, what type of mistake could they have made? A) Do not reject Ho; Type I error B) C) Do not reject Ho; Type II error Reject Ho: Type I error D) Reject Ho; Type IIl error 5. A newspaper is conducting a statewide survey concerning the race for governor. The newspaper will take a simple random sample of n registered voters and determine X the number of voters that will vote for the Democratic candidate. Is there evidence that a clear majority of the population will vote for the Democratic candidate? To answer this, they will test the hypotheses H: p = 0.50 versus Ha: p > 0.50. If n = 1200 and X = 640, what is the P-value for this hypothesis test? A) Less than 0.0002 B) 0.0105 C) 0.0330 D) 0.2326 6. A study was conducted at the University of Waterloo on the impact characteristics of football helmets used in competitive high school programs. There were three types of helmets considered, classified according to liner type: suspension, padded-suspension, and padded. In the study, a measurement called the Gadd Severity Index (GSl) was obtained on each helmet, using a standardized impact test. A helmet was deemed to have failed if the GSI was greater than 1200. Of the 81 helmets tested, 29 failed the GSI 1200 criterion. How many suspension-type helmets should be tested so that the margin of error does not exceed 0.05 with 95% confidence? A) 385 B) 20 C) 271 D) 250 E) 82
Explanation / Answer
Ans:
4)
sample proportion=0.64
sample size,n=100
Test statistic:
z=(0.64-0.5)/sqrt(0.5*0.5/100)=2.8
critical z value=1.645
As,z=2.8>1.645,so we reject H0.
When we reject H0,but H0 is true,we make type I error.
Option C is correct(Reject H0,type I error)
5)
sample proportion=640/1200=0.533
sample size,n=1200
Test statistic:
z=(0.533-0.5)/sqrt(0.5*0.5/1200)=2.31
p-value=P(z>2.31)=0.0104
Option B is correct.
6)
sample proportion=29/81=0.358
sample size required=1.96^2*0.358*(1-0.358)/0.05^2=367.75
Option A is correct.