1) In a recent study of 35 ninth-grade students, the mean number of hours per we
ID: 3311917 • Letter: 1
Question
1) In a recent study of 35 ninth-grade students, the mean number of hours per week they played video games was 16. The standard deviation of the population was 3.0.
a. Find the best point estimate of the population mean. ________________________
b. Find the 95% confidence interval of the mean time playing video games. (round to 2 places) ________________________
2) A recent study of 10 randomly selected employees of a company showed that the mean of the distance they traveled to work was 14 miles. The standard deviation of the sample mean was 2.0 miles. Find the 95% confidence interval of the true mean. (round to 2 places) ________________________
3) A random sample of college students who owned cars revealed the following: out of 120 cars, 24 had a manual transmission. Determine a 90% confidence interval for the true proportion of cars with a manual transmissions. (round to 2 places) ________________________
4) Nationally the mean cost of building a home is $117 per square foot with a standard deviation of $20. A random sample of 36 new homes in the south indicated that the mean cost was $123. Test the claim that the true mean has increased. Use a 0.10 level of significance.
1) What are the Hypotheses: H0: ____________ H1: _____________ 2) Calculate the test value: _______________ 3) Graph the critical region: 4) Conclusion:
5) The average strawberry has approximately 200 seeds. A very patient student selected a random sample of 10 strawberries and found a sample mean of 185 seeds with a standard deviation of 10. Test the claim that the true mean is less than 200. Use a 0.01 level of significance.
1) What are the Hypotheses: H0: ____________ H1: _____________ 2) Calculate the test value: _______________ 3) Graph the critical region: 4) Conclusion:
6) Nationally the average cost of building a home is $117 per square foot. A random sample of 36 new homes in the south indicated that the mean cost was $123 and standard deviation of $20 Test the claim that the true mean is different. Use a 0.05 level of significance.
1) What are the Hypotheses: H0: ____________ H1: _____________ 2) Calculate the test value: _______________ 3) Graph the critical region: 4) Conclusion:
7) Currently 50% of Seniors plan on attending college. In a recent sample of 25 high school seniors, 15 indicated they plan on attending college. You believe the proportion of Seniors planning on attending college is increasing. Test your claim using a 0.05 level of significance.
1) What are the Hypotheses: H0: ____________ H1: _____________ 2) Calculate the test value: _______________ 3) Graph the critical region: 4) Conclusion:
Explanation / Answer
Solution:
1) In a recent study of 35 ninth-grade students, the mean number of hours per week they played video games was 16. The standard deviation of the population was 3.0.
a. Find the best point estimate of the population mean. ________________________
b. Find the 95% confidence interval of the mean time playing video games. (round to 2 places)
the best point estimate of the population mean=sample mean
=16
. Find the 95% confidence interval of the mean time playing video games.
z for 95%=1.96
since population standard deviation is given
use z crit
95% confdience interval is
samplemean-zcrit(pop stddev/sqrt(n),samplemean+zcrit(pop stddev/sqrt(n)
16-1.96(3/sqrt(35),16+1.96(3/sqrt(35),
15.0061,16.9939
15.01<mu<16.99
lower limit=15.01
upper limit=16.99
we are 95% confident that the true population mean lies in between 15.01 and 16.99
Solution2:
2) A recent study of 10 randomly selected employees of a company showed that the mean of the distance they traveled to work was 14 miles. The standard deviation of the sample mean was 2.0 miles. Find the 95% confidence interval of the true mean. (round to 2 places)
z crit=95%=1.96
95% confidence interval of the true mean.
samplemean-zcrit(pop stddev/sqrt(n),samplemean+zcrit(pop stddev/sqrt(n)
=14-1.96(2/sqrt(10),14+1.96(2/sqrt(10)
=12.76,15.24
12.76<mu<15.24
lower limit=12.76
upper limit=15.24
we are 95% confident that the true mean lies in between 12.76 and 15.24
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