Question

PROBLEM 4. 15 pts: Test H0: mu = 70 vs. H1: mu > 70

1. n= 9 sample mean = 75 sigma = 5.        Alpha =.05
2. n= 9 sample mean = 75 S = 5.        Alpha =.05
3. n=100 items 40 defective. H0: p= .3 vs. H1: p > .3 Alpha=.05

Answer 1

1. Here we want to test

H₀:=70 v/s 70

Here, n=9

sample mean =75

=5

level of significance =0.05

The test statistic Z is given by,

or,

P value from table = 0.001

here,since 0.001<0.05

i.e. p value<

We reject the null hypothesis.

2.

Here we want to test

H₀:=70 v/s 70

Here, n=9

sample mean =75

sample sd= s =5

level of significance =0.05

The test statistic T is given by,

or,

Degrees of freedom = n-1=9-1=8

P value from table = 0.009

here,since 0.009<0.05

i.e. p value<

We reject the null hypothesis.

3. here we want to test,

H0: p= .3 vs. H1: p > .3

Let the population proportion be and sample proportion be p₀

level of significance =0.05

Here n=100

=0.3

p₀=0.4

The test statistic

T=-2.04

p-value =0.021

here,since 0.021<0.05

i.e. p value<

We reject the null hypothesis.