It is believed that 11% of all Americans are left-handed. A college needs to know how many left-handed desks to place in the big lecture halls being constructed on its campus. In a random sample of 100 students of its 10376 students, 14 were left-handed. Does this provide enough evidence to show that students at this college have a higher percentage of left-handers than the general American population? Use a 10% level of significance.P: PARAMETER What is the correct parameter symbol for this problem? What is the wording of the parameter in the context of this problem? H: HYPOTHESES Fill in the correct null and alternative hypotheses: 𝐻0: 𝐻𝐴: A: ASSUMPTIONS Since information was collected from each object, what conditions do we need to check? Check all that apply. σσ is unknown.𝑛(1-𝑝)≥10σσ is known.𝑛(1-𝑝̂)≥10𝑛(𝑝̂)≥10𝑛𝑝≥10𝑛≥30 or normal population.𝑁≥20𝑛 Check those assumptions: 1. 𝑛𝑝 = which is 2. 𝑛(1-𝑝) = which is 3. 𝑁 = which is If no N is given in the problem, use 1000000N: NAME THE PROCEDURE The conditions are met to use a .T: TEST STATISTIC The symbol and value of the random variable on this problem are as follows: Leave this answer as a fraction. = The formula set up of the test statistic is as follows.: (Leave any values that were given as fractions as fractions) 𝑧=𝑝̂-𝑝𝑝(1-𝑝)𝑛=( - )/(( ⋅(1- )) / ) Final answer for the test statistic from technology. Round to 2 decimal places: z = O: OBTAIN THE P-VALUE Report to 4 decimal places. It is possible when rounded that a p-value is 0.0000 P-value = M: MAKE A DECISION Since the p-value , we .S: STATE A CONCLUSION There significant evidence to conclude
Question
It is believed that 11% of all Americans are left-handed. A college needs to know how many left-handed desks to place in the big lecture halls being constructed on its campus. In a random sample of 100 students of its 10376 students, 14 were left-handed. Does this provide enough evidence to show that students at this college have a higher percentage of left-handers than the general American population? Use a 10% level of significance.P: PARAMETER What is the correct parameter symbol for this problem? What is the wording of the parameter in the context of this problem? H: HYPOTHESES Fill in the correct null and alternative hypotheses: 𝐻0: 𝐻𝐴: A: ASSUMPTIONS Since information was collected from each object, what conditions do we need to check? Check all that apply. σσ is unknown.𝑛(1-𝑝)≥10σσ is known.𝑛(1-𝑝̂)≥10𝑛(𝑝̂)≥10𝑛𝑝≥10𝑛≥30 or normal population.𝑁≥20𝑛 Check those assumptions: 1. 𝑛𝑝 = which is 2. 𝑛(1-𝑝) = which is 3. 𝑁 = which is If no N is given in the problem, use 1000000N: NAME THE PROCEDURE The conditions are met to use a .T: TEST STATISTIC The symbol and value of the random variable on this problem are as follows: Leave this answer as a fraction. = The formula set up of the test statistic is as follows.: (Leave any values that were given as fractions as fractions) 𝑧=𝑝̂-𝑝𝑝(1-𝑝)𝑛=( - )/(( ⋅(1- )) / ) Final answer for the test statistic from technology. Round to 2 decimal places: z = O: OBTAIN THE P-VALUE Report to 4 decimal places. It is possible when rounded that a p-value is 0.0000 P-value = M: MAKE A DECISION Since the p-value , we .S: STATE A CONCLUSION There significant evidence to conclude
Solution
P: PARAMETER The correct parameter symbol for this problem is p. The wording of the parameter in the context of this problem is "the proportion of all students at the college who are left-handed."
H: HYPOTHESES Null hypothesis, H0: p = 0.11 Alternative hypothesis, HA: p > 0.11
A: ASSUMPTIONS The conditions we need to check are:
- n(1-p)≥10
- n(p)≥10
- N≥20n
Check those assumptions:
- np = 100*0.11 = 11 which is greater than 10.
- n(1-p) = 100*(1-0.11) = 89 which is greater than 10.
- N = 10376 which is greater than 20*100 = 2000.
N: NAME THE PROCEDURE The conditions are met to use a one-sample z-test for a proportion.
T: TEST STATISTIC The symbol and value of the random variable on this problem are as follows: p̂ = 14/100 = 0.14 The formula set up of the test statistic is as follows: z = (p̂ - p) / sqrt [ p(1 - p) / n ] = (0.14 - 0.11) / sqrt [ 0.11(1 - 0.11) / 100 ] Final answer for the test statistic from technology. Round to 2 decimal places: z = 1.03
O: OBTAIN THE P-VALUE P-value = 0.1510
M: MAKE A DECISION Since the p-value (0.1510) is greater than the level of significance (0.10), we fail to reject the null hypothesis.
S: STATE A CONCLUSION There is not significant evidence to conclude that the proportion of left-handed students at the college is greater than the general American population.
Similar Questions
It is believed that 11% of all Americans are left-handed. A college needs to know how many left-handed desks to place in the big lecture halls being constructed on its campus. In a random sample of 370 students from that college, whether or not a student was left-handed was recorded for each student. The college wants to know if the data provide enough evidence to show that students at this college have a different percentage of left-handers than the general American population? State the random variable, population parameter, and hypotheses. State the Type I and Type II errors in the context of this problem.a) The symbol for the random variable involved in this problem is Incorrect
It is believed that 11% of all Americans are left-handed. In a random sample of 500 students from a particular college with 52407 students, 47 were left-handed. Find a 97% confidence interval for the percentage of all students at this particular college who are left-handed.P: Parameter What is the correct parameter symbol for this problem? What is the wording of the parameter in the context of this problem? A: AssumptionsSince information was collected from each object, what conditions do we need to check? Check all that apply. 𝑛≥30 or normal population.σσ is known.𝑛(1-𝑝)≥10𝑛(𝑝̂)≥10σσ is unknown.𝑁≥20𝑛𝑛(1-𝑝̂)≥10𝑛𝑝≥10 Check those assumptions: 1. 𝑛𝑝^= which is 2. 𝑛(1-𝑝^)= which is 3. 𝑁= which is If no N is given in the problem, use 1000000N: Name the procedure The conditions are met to use a .I: Interval and point estimate The symbol and value of the point estimate on this problem are as follows: = Leave answer as a fraction. The interval estimate for is ( , ) Round endpoints to 3 decimal places.C: Conclusion We are % confident that the is between % and %
According to previous studies, 16% of the U.S. population is left-handed. Not knowing this, a high school student claims that the percentage of left-handed people in the U.S. is 15%.The student is going to take a random sample of 2100 people in the U.S. to try to gather evidence to support the claim. Let p be the proportion of left-handed people in the sample.Answer the following. (If necessary, consult a list of formulas.)(a)Find the mean of p.(b)Find the standard deviation of p.(c)Compute an approximation for P≥p0.15, which is the probability that there will be 15% or more left-handed people in the sample. Round your answer to four decimal places.
A hypothesis test is done in which the alternative hypothesis is that more than 10% of the population is left-handed.The p-value for the test is calculated to be 0.18Assume an 85% confidence level, Which statement is correct?
In 2001, the polls found that 81% of American adults believed that there was a conspiracy in the death of President Kennedy. Assume a recent poll asked 1740 American adults if they believe there was a conspiracy in the assassination and it found that 1374 believe there was a conspiracy. Does the data show that the proportion of Americans who believe in this conspiracy is now lower? Test at the 5% level.P: PARAMETER What is the correct parameter symbol for this problem? What is the wording of the parameter in the context of this problem? H: HYPOTHESES Fill in the correct null and alternative hypotheses: 𝐻0: 𝐻𝐴: A: ASSUMPTIONS Since information was collected from each object, what conditions do we need to check? Check all that apply. 𝑛(𝑝̂)≥10𝑁≥20𝑛𝑛𝑝≥10𝑛(1-𝑝)≥10𝑛(1-𝑝̂)≥10σσ is known.𝑛≥30 or normal population.σσ is unknown. Check those assumptions: 1. 𝑛𝑝 = which is 2. 𝑛(1-𝑝) = which is 3. 𝑁 = which is If no N is given in the problem, use 1000000N: NAME THE PROCEDURE The conditions are met to use a .T: TEST STATISTIC The symbol and value of the random variable on this problem are as follows: Leave this answer as a fraction. = The formula set up of the test statistic is as follows.: (Leave any values that were given as fractions as fractions) 𝑧=𝑝̂-𝑝𝑝(1-𝑝)𝑛=( - )/(( ⋅(1- )) / ) Final answer for the test statistic from technology. Round to 2 decimal places: z = O: OBTAIN THE P-VALUE Report to 4 decimal places. It is possible when rounded that a p-value is 0.0000 P-value = M: MAKE A DECISION Since the p-value , we .S: STATE A CONCLUSION There significant evidence to conclude
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