The price to earnings ratio (P/E) is an important tool in financial work. A rand
ID: 3231869 • Letter: T
Question
The price to earnings ratio (P/E) is an important tool in financial work. A random sample of 14 large U.S. banks (J. P. Morgan, Bank of America, etc) gave the following P/E ratios.
24, 16, 22, 14, 12, 13, 17, 22, 15, 19, 23, 13, 11, 18
Generally speaking, a low P/E ratio indicates a "value" or bargain stock. Financial publications indicated that the P/E ratio of the S&P 500 stock index has typically been 19.6. Let x be a random variable representing the P/E ratio of all large U.S. bank stocks. We assume that x has a normal distribution and = 3.9. Do these data indicate that the P/E ratio of all U.S. bank stocks is less than 19.6? Use = 0.10.
(a) Enter the following.
x =
s =
(b) Identify the claim, the null hypothesis, and the alternative hypothesis.
(c) Will you use a left-tailed, right-tailed, or two-tailed test?
two-tailed
left-tailed
right-tailed
(d) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
The standard normal, since we assume that x has a normal distribution with unknown .
The standard normal, since n is large with known .
The Student's t, since we assume that x has a normal distribution with known .
The standard normal, since n is large with unknown .
The Student's t, since n is large with unknown .
The standard normal, since we assume that x has a normal distribution with known .
(e) Sketch the sampling distribution showing the area corresponding to the approximate P-value.
(f) Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ?
At the = 0.10 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
At the = 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant.
At the = 0.10 level, we reject the null hypothesis and conclude the data are statistically significant.
At the = 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
(g) State your conclusion in the context of the application.
Fail to reject the null hypothesis, there is insufficient evidence that average P/E for large banks is less than the S&P 500 Index.
Fail to reject the null hypothesis, there is sufficient evidence that average P/E for large banks is less than the S&P 500 Index.
Reject the null hypothesis, there is insufficient evidence that average P/E for large banks is less than the S&P 500 Index.
Reject the null hypothesis, there is sufficient evidence that average P/E for large banks is less than the S&P 500 Index.
Claim: > < = 19.6 Ho: > < = 19.6 H1: > < = 19.6Explanation / Answer
Given that,
population mean(u)=19.6
standard deviation, =3.9
sample mean, x =17.0714
number (n)=14
null, Ho: =19.6
alternate, H1: <19.6
level of significance, = 0.1
from standard normal table,left tailed z /2 =1.282
since our test is left-tailed
reject Ho, if zo < -1.282
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 17.0714-19.6/(3.9/sqrt(14)
zo = -2.42594
| zo | = 2.42594
critical value
the value of |z | at los 10% is 1.282
we got |zo| =2.42594 & | z | = 1.282
make decision
hence value of | zo | > | z | and here we reject Ho
p-value : left tail - ha : ( p < -2.42594 ) = 0.00763
hence value of p0.1 > 0.00763, here we reject Ho
ANSWERS
---------------
null, Ho: =19.6
alternate, H1: <19.6
test statistic: -2.42594
critical value: -1.282
decision: reject Ho
p-value: 0.00763
left-tailed
The standard normal, since n is large with known
At the = 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant.
Reject the null hypothesis, there is insufficient evidence that average P/E for large banks is less than the S&P 500 Index
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.