Question

Very important homework for me ...

2.) A process produces cable for the local telephone company. When the process is operating correctly, cable diameter follows a normal distribution with mean 4 inches. A random sample of 48 pieces of cable found diameters with a sample mean of 7 inches and a sample standard deviation of 0,66 inches.

a) State your hypothesis H0 and H1 claiming that the process is operating correctly.

b) State the decision rule, sample statistics, table value and test statistic in the same order as in the extra solved examples on hypothesis testing.

c) Test, at the 99% level, the null hypothesis that the process is operating correctly

Answer 1

Answer:

n= 48,  = 4

= 7 , s = 0.66

c= 99% = 0.99 ,

= 1 - c = 1- 0.99 = 0.01

a)

null and alternative hypothesis is

Ho:   = 4

H1:   4

b)

Calculate t critical value for two tailed test with = 0.01

and df = n -1 = 48 -1 = 47

using t table we get critical values as

Critical value = 2.690

decision rule is

Reject Ho if ( test statistics ) < ( -2.690 ) or if ( test statistics ) > ( 2.690 )

Rejection region is as follows,

formula for test statistics is

t = 31.4918

test statistics: t = 31.492

c)

here, ( test statistics = 31.492 ) > ( Critical value = 2.690)

Hence,

Null hypothesis is rejected.

there is NOT sufficient evidence to support the null hypothesis that the process is operating correctly