A popular blog reports that 42% of college students use Twitter. The director of media relations...

A popular blog reports that 42% of college students use Twitter. The director of media relations at a large university thinks that the proportion may be different at her university. She polls a simple random sample of 200 students, and 101 of them report that they use Twitter. Can she conclude that the proportion of students at her university who use Twitter differs from 0.42? Answer by showing the five steps of signigicance test, allowing a Type I error rate of 0.05.

Solutions

Expert Solution

Given that,
possibile chances (x)=101
sample size(n)=200
success rate ( p )= x/n = 0.505
success probability,( po )=0.42
failure probability,( qo) = 0.58
null, Ho:p=0.42
alternate, H1: p!=0.42
level of significance, α = 0.05
from standard normal table, two tailed z α/2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.505-0.42/(sqrt(0.2436)/200)
zo =2.4355
| zo | =2.4355
critical value
the value of |z α| at los 0.05% is 1.96
we got |zo| =2.436 & | z α | =1.96
make decision
hence value of | zo | > | z α| and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 2.43554 ) = 0.01487
hence value of p0.05 > 0.0149,here we reject Ho
ANSWERS
---------------
null, Ho:p=0.42
alternate, H1: p!=0.42
test statistic: 2.4355
critical value: -1.96 , 1.96
decision: reject Ho
p-value: 0.01487
we have enough evidence to support the claim that the proportion of students at her university who use Twitter differs from 0.42
type 1 error is possible because it reject the null hypothesis.

orchestra answered 1 year ago

Next > < Previous

Related Solutions

By 2009, social media services, such as Facebook and Twitter, had become a popular marketing tool...

By 2009, social media services, such as Facebook and Twitter, had become a popular marketing tool for small businesses. In fact, almost 25% of firms with fewer than 100 employees were using social media for marketing purposes. This was more than double the percentage of the prior year. Many of these firms cite the ease of use and low cost of these social media as the main reason for using them for reaching out to and communicating with potential and...

Binge drinking on college campuses has been a hot topic in the popular media and in...

Binge drinking on college campuses has been a hot topic in the popular media and in scholarly research. Flett, Goldstein, Wall, Hewitt, Wekerle, and Azzi (2008) report the results of a study relating perfectionism to binge drinking. In the study, students were classified inot three groups based on the number of binge drinking episondes they experienced during the past month (0, 1, 2+). The students then completed a perfectionism questionnaire including one scale measuring parental criticism. One sample item is...

Highland Company produces a lightweight backpack that is popular with college students

Highland Company produces a lightweight backpack that is popular with college students. Standard variable costs relating to a single backpack are given below Standard Quantity or HoursStandard Price or RateStandard CostDirect materials?$4.00 per yard$?Direct labor???Variable manufacturing overhead?$2 per direct labor-hourTotal standard cost per unit?Overhead is applied to production on the basis of direct labor-hours. During March, 700 backpacks were manufactured and sold. Selected information relating to the month's production is given below: MaterialsUsedDirect LaborVariableManufacturingOverheadTotal standard cost allowed*$11,200$10,500$2,100Actual costs incurred$8,925?$4,032Materials price variance?Materials quantity variance$700ULabor rate...

Problems 6-10: In 2015 about 60% of college students used Twitter. In a recent study of...

Problems 6-10: In 2015 about 60% of college students used Twitter. In a recent study of 100 students, 80 now use Twitter. Is this evidence to think the percent has changed? We wish to conduct a hypothesis test with 5% significance. 6) State the null and alternative hypothesis. 7) Find the test statistic and P-value and report those values here: 8) What is the decision and conclusion? 9) Now, construct a 95% confidence interval using the sample of 100 students...

Problems 6-10: In 2015 about 60% of college students used Twitter. In a recent study of...

Problems 6-10: In 2015 about 60% of college students used Twitter. In a recent study of 100 students, 80 now use Twitter. Is this evidence to think the percent has changed? We wish to conduct a hypothesis test with 5% significance. State the null and alternative hypothesis. Find the test statistic and P-value and report those values here: What is the decision and conclusion? Now, construct a 95% confidence interval using the sample of 100 students and 80 saying they...

Contrary to popular media reports, scientists rarely prove a theory. Instead, the language of science requires...

Contrary to popular media reports, scientists rarely prove a theory. Instead, the language of science requires a person to report that a theory is supported, partially supported, or not supported. Based on your knowledge of statistics, explain why the scientific community uses this language.

The director of admissions of a small college selected 120 students at random from the new...

The director of admissions of a small college selected 120 students at random from the new freshman class in a study to determine whether a student's grade point average (gpa) at the end of freshman year can be predicted from the ACT test score. (a) Read in the dataset (it is in the le named ACT.txt ). (b) Obtain the least-squares estimates of intercept and slope, and state the estimated regression function. (c) Plot the data and the estimated regression...

The director of admissions of a small college selected 120 students at random from the new...

The director of admissions of a small college selected 120 students at random from the new freshman class in a study to determine whether a student’s grade point average (GPA) at the end of the freshman year (y) can be predicted from the ACT test score (x1). GPA ACT ITS RP 3.897 21 122 99 3.885 14 132 71 3.778 28 119 95 2.540 22 99 75 3.028 21 131 46 3.865 31 139 77 2.962 32 113 85...

An admissions director wants to estimate the mean age of all students enrolled at a college....

An admissions director wants to estimate the mean age of all students enrolled at a college. The estimate must be within 1 years of the population mean. Assume the population of ages is normally distributed and the population standard deviation is 9.5 years. Determine the minimum sample size required to construct a 80% confidence interval for the population mean age. Determine the minimum sample size required to construct a 95% confidence interval for the population mean age. Which level of...

It has been reported that 42% of college students graduate in 4 years. Consider a random...

It has been reported that 42% of college students graduate in 4 years. Consider a random sample of thirty students, and let the random variable X be the number who graduate in 4 years. Find the probability that 14 or fewer students in the sample graduate in 4 years.

Subjects