Test the folowing claim ldentiy the nul hypothesis, allernative hypothes, test s

Question

Test the folowing claim ldentiy the nul hypothesis, allernative hypothes, test statistic,cntical value(s), conclusion about the null hypothesis, and final conclusion that addresses the oniginal claim A simple random sample ot 45 salaries of professional football coaches has a mean of $413,137. The standard deviation of all salaries of professional football coaches s $461,155 Use a 0 05 significance level to test the claim that the mean salary of a professional football coach is less than $500,000 What are the nulil and alternative hypotheses? O A. Ho ·$500,000 ° C. h6 ( $500,000 O B. Hop>$500,000 H,

Explanation / Answer

Given that,
population mean(u)=500000
standard deviation, =461155
sample mean, x =413137
number (n)=45
null, Ho: =500000
alternate, H1: <500000
level of significance, = 0.05
from standard normal table,left tailed z /2 =1.645
since our test is left-tailed
reject Ho, if zo < -1.645
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 413137-500000/(461155/sqrt(45)
zo = -1.26
| zo | = 1.26
critical value
the value of |z | at los 5% is 1.645
we got |zo| =1.26 & | z | = 1.645
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value : left tail - ha : ( p < -1.26 ) = 0.1
hence value of p0.05 < 0.1, here we do not reject Ho
ANSWERS
---------------
null, Ho: =500000
alternate, H1: <500000
test statistic: -1.26
critical value: -1.645
decision: do not reject Ho
p-value: 0.1

no evidence to support the claim

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.