Question 1 of 19The National Assessment of Educational Progress (NAEP) includes a mathematics test for eighth‑grade students. Scores on the test range from 0 to 500 . Demonstrating the ability to use the mean to solve a problem is an example of the skills and knowledge associated with performance at the Basic level. An example of the knowledge and skills associated with the Proficient level is being able to read and interpret a stem‑and‑leaf plot.In 2015, 136,900 eighth‑graders were in the NAEP sample for the mathematics test. The mean mathematics score was x¯=282 . We want to estimate the mean score μ in the population of all eighth‑graders. Consider the NAEP sample as an SRS from a Normal population with standard deviation σ=110 .(a) If we take many samples, the sample mean x¯ varies from sample to sample according to a Normal distribution with mean equal to the unknown mean score μ in the population. What is the standard deviation of this sampling distribution? (Enter your answer rounded to four decimal places.)standard deviation =  (b) According to the 95 part of the 68‑95‑99.7 rule, 95% of all values of x¯ fall within how many points on either side of the unknown mean μ ? (Enter your answer rounded to four decimal places.)

Question
Asked Nov 9, 2019
29 views

Question 1 of 19

The National Assessment of Educational Progress (NAEP) includes a mathematics test for eighth‑grade students. Scores on the test range from 0 to 500 . Demonstrating the ability to use the mean to solve a problem is an example of the skills and knowledge associated with performance at the Basic level. An example of the knowledge and skills associated with the Proficient level is being able to read and interpret a stem‑and‑leaf plot.

In 2015, 136,900 eighth‑graders were in the NAEP sample for the mathematics test. The mean mathematics score was x¯=282 . We want to estimate the mean score μ in the population of all eighth‑graders. Consider the NAEP sample as an SRS from a Normal population with standard deviation σ=110 .

(a) If we take many samples, the sample mean x¯ varies from sample to sample according to a Normal distribution with mean equal to the unknown mean score μ in the population. What is the standard deviation of this sampling distribution? (Enter your answer rounded to four decimal places.)

standard deviation =
 
 
(b) According to the 95 part of the 68‑95‑99.7 rule, 95% of all values of x¯ fall within how many points on either side of the unknown mean μ ? (Enter your answer rounded to four decimal places.)
 
check_circle

Expert Answer

Step 1

a)

Standard deviation of sampling distribution:

...
help_outline

Image Transcriptionclose

Vn 110 136,900 0.2973

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Statistics

Hypothesis Testing

Related Statistics Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: Question 15 is what I am struggling with. Please help, thank you.

A: The hypotheses are given below:

question_answer

Q: Statistics Question

A: 1) The interpretation from the estimated coefficient of the SodaTax can be explained as:Let SodaTax_...

question_answer

Q: Steps 1,2, and three

A: Step 1:The hypotheses are given below:Null hypothesis:H0: There is no association between method of ...

question_answer

Q: The weight of a type of dog follows Normal distribution with mean of 10 pounds and standard deviatio...

A: It is given that the weight of dog is normally distributed with mean 10 pounds and standard deviatio...

question_answer

Q: Please help me with this problem

A: Given information,A survey of 300 union members in New York State reveals that 112 favor the republi...

question_answer

Q: 72% of owned dogs in the United States are spayed or neutered. Round your answers to four decimal pl...

A: a.The probability that exactly 26 of them are spayed or neutered is obtained below:From the given in...

question_answer

Q: Notes: ** indicates that the estimates are statistically significant at the 5 percent level. M...

A: Hey, since there are multiple subpart questions posted, we will answer first two subpart questions. ...

question_answer

Q: According to the CTIA-The Wireless Association, the mean monthly revenue per cellphone was $48.79 in...

A: (a)The null and alternative hypotheses is,Null hypothesis:H0: µ=48.79That is, the mean monthly reven...

question_answer

Q: A study of 25 graduates of four-year public colleges revealed the mean amount owed by a student in s...

A: It is given that the mean amount owed by a student in student loans is $55,051. The sample standard ...