A random sample of 76 eighth grade​ students' scores on a national mathematics assessment test has a mean score of 267. This test result prompts a state school administrator to declare that the mean score for the​ state's eighth graders on this exam is more than 260. Assume that the population standard deviation is 33. At α=0.11​, is there enough evidence to support the​administrator's claim? Complete parts​ (a) through​ (e).

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Topic Video
Question

A random sample of 76 eighth grade​ students' scores on a national mathematics assessment test has a mean score of 267. This test result prompts a state school administrator to declare that the mean score for the​ state's eighth graders on this exam is more than 260.

Assume that the population standard deviation is 33.

At α=0.11​, is there enough evidence to support the​administrator's claim? Complete parts​ (a) through​ (e).

A random sample of 76 eighth grade students' scores on a national mathematics assessment test has a mean score of 267. This test result prompts a state school administrator to declare
that the mean score for the state's eighth graders on this exam is more than 260. Assume that the population standard deviation is 33. At a = 0.11, is there enough evidence to support the
administrator's claim? Complete parts (a) through (e).
(a) Write the claim mathematically and identify Ho and Ha. Choose the correct answer below.
Ο Α. H: μ2 260 (claim)
O B. Ho: µ= 260 (claim)
Ha:µ > 260
O C. Ho: µs 260 (claim)
Ha: µ> 260
Ha:µ<260
O D. Ho: µ = 260
Ha: µ> 260 (claim)
O E. Ho: µs260
Ha: µ> 260 (claim)
O F. Ho: µ<260
Ha: µ2 260 (claim)
(b) Find the standardized test statistic z, and its corresponding area.
(Round to two decimal places as needed.)
(c) Find the P-value.
P-value =|(Round to three decimal places as needed.)
(d) Decide whether to reject or fail to reject the null hypothesis.
Reject Ho
Fail to reject Ho
(e) Interpret your decision in the context of the original claim.
At the 11% significance level, there
V enough evidence to
the administrator's claim that the mean score for the state's eighth graders on the exam is more than 260.
Transcribed Image Text:A random sample of 76 eighth grade students' scores on a national mathematics assessment test has a mean score of 267. This test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than 260. Assume that the population standard deviation is 33. At a = 0.11, is there enough evidence to support the administrator's claim? Complete parts (a) through (e). (a) Write the claim mathematically and identify Ho and Ha. Choose the correct answer below. Ο Α. H: μ2 260 (claim) O B. Ho: µ= 260 (claim) Ha:µ > 260 O C. Ho: µs 260 (claim) Ha: µ> 260 Ha:µ<260 O D. Ho: µ = 260 Ha: µ> 260 (claim) O E. Ho: µs260 Ha: µ> 260 (claim) O F. Ho: µ<260 Ha: µ2 260 (claim) (b) Find the standardized test statistic z, and its corresponding area. (Round to two decimal places as needed.) (c) Find the P-value. P-value =|(Round to three decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis. Reject Ho Fail to reject Ho (e) Interpret your decision in the context of the original claim. At the 11% significance level, there V enough evidence to the administrator's claim that the mean score for the state's eighth graders on the exam is more than 260.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Hypothesis Tests and Confidence Intervals for Means
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman