Question

In: Statistics and Probability

The state education commission wants to estimate the fraction of tenth grade students that have reading...

The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level.

Step 2 of 2 :  

Suppose a sample of 1382 tenth graders is drawn. Of the students sampled, 996 read above the eighth grade level. Using the data, construct the 99% Confidence interval for the population proportion of tenth graders reading at or below the eighth grade level. Round your answers to three decimal places.

THANK YOU

Solutions

Expert Solution

Solution :

Given that,

n = 1382

x = 996

Point estimate = sample proportion = = x / n = 0.721

1 - = 0.279

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 2.576 * (((0.721*0.279) / 1382)

= 0.031

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.721 - 0.031 < p < 0.721 + 0.031

0.690 < p < 0.752

The 99% confidence interval is : (0.690 , 0.752)


Related Solutions

The state education commission wants to estimate the fraction of tenth grade students that have reading...
The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. Step 1 of 2: Suppose a sample of 1132 tenth graders is drawn. Of the students sampled, 816 read above the eighth grade level. Using the data, estimate the proportion of tenth graders reading at or below the eighth grade level. Enter your answer as a fraction or a decimal number rounded to three decimal places....
The state education commission wants to estimate the fraction of tenth grade students that have reading...
The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. Step 2 of 2 :   Suppose a sample of 966 tenth graders is drawn. Of the students sampled, 802 read above the eighth grade level. Using the data, construct the 98% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level. Round your answers to three decimal places.
The state education commission wants to estimate the fraction of tenth grade students that have reading...
The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. Step 2 of 2: Suppose a sample of 1042 tenth graders is drawn. Of the students sampled, 865 read above the eighth grade level. Using the data, construct the 90% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level. Round your answers to three decimal places.
The state education commission wants to estimate the fraction of tenth grade students that have reading...
The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. Step 2 of 2 :   Suppose a sample of 333 tenth graders is drawn. Of the students sampled, 254 read above the eighth grade level. Using the data, construct the 80% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level. Round your answers to three decimal places.
The state education commission wants to estimate the fraction of tenth grade students that have reading...
The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. Step 2 of 2 :   Suppose a sample of 801 tenth graders is drawn. Of the students sampled, 577 read above the eighth grade level. Using the data, construct the 95%confidence interval for the population proportion of tenth graders reading at or below the eighth grade level. Round your answers to three decimal places.
The state education commission wants to estimate the fraction of renth grade students that have reading...
The state education commission wants to estimate the fraction of renth grade students that have reading skills below the eighth grade level. Step 2 of 2: Suppose a sample of 1649 tenth graders is drawn. Of the students sampled, 1270 read above the eighth grade level. Using the data construct the 95% interval for the population proportion of tenth graders reading at or below the eighth level. Round your answers to three decimal places.
A psychological test was standardized for a population of tenth-grade students in such a way that...
A psychological test was standardized for a population of tenth-grade students in such a way that the mean must be 500 and the standard deviation must be 100. A sample of 90 twelfth-grade students was selected independently and at random, and each given the test. The sample mean turned out to be 506.7. On this basis, can one say that the population distribution for twelfth grade students would differ from that of tenth-graders?
A psychologist wants to study whether 6th grade or 10th grade students have more empathy for...
A psychologist wants to study whether 6th grade or 10th grade students have more empathy for others. Which method of research would you prefer to have used: cross-sectional or longitudinal? Explain your preference.
An education researcher is interested in students’ performance on a standardised reading test.
An education researcher is interested in students’ performance on a standardised reading test. The researcher believes that if students experience a particular form of positive coaching, then they will be more likely to perform better on the reading test. This researcher is testing two hypotheses. The first is that the coaching boosts self-efficacy and has an effect on students’ reading test scores. The second is that this treatment effect is moderated by year in school. Past research has suggested that...
The reading speed of second grade students in a large city is approximately​ normal, with a...
The reading speed of second grade students in a large city is approximately​ normal, with a mean of 88 words per minute​ (wpm) and a standard deviation of 10 wpm. Complete parts​ (a) through​ (f). ​(a) What is the probability a randomly selected student in the city will read more than 92 words per​ minute?The probability is ​(Round to four decimal places as​ needed.) Interpret this probability. Select the correct choice below and fill in the answer box within your...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT