Consider the following hypotheses: H0: mean = 5 H1: mean < 5 A test is performed with a sample of size 25. The sample mean was 4.73 and the population standard deviation is 1…

Question

asked Nov 10, 2020 176k views

1 Answer

Tom Verhoeff · Answer 1 · 2020-11-15T10:30:05+0000

Answer:

0.1406.

Explanation:

Given :
$H_o:\mu = 5$

$H_1:\mu < 5$

To Find : compute the P-value.

Solution:

Sample size = 25

n < 30

So, we will go for t-test

Now we are given that the population standard deviation is 1.2.

$\sqrt{(s)/(n)}=1.2$ Where s is the variance

$\sqrt{(s)/(25)}=1.2$

√(s)=6

s = 6^2

s = 36

So, the variance is 36

we require sample standard deviation for t test

So, Sample standard deviation =
$\sqrt{(s)/(n-1)}$

=
$\sqrt{(36)/(25-1)}$

=
1.2247

Formula of t-test =
$(m-\mu)/((s)/(√(n)))$

Where s is the standard deviation of sample

Sample mean = 4.73

Mean =
$\mu = 5$

s = 1.2247

n =25

So,
t=(5-4.73)/((1.2247)/(√(25)))

t=1.1023

So, p value with respect to t-table is 0.1406.

Hence p-value is 0.1406.