A rods manufacturer makes rods with a length that is supposed to be 11 inches. A quality control technician sampled 40 rods and found that the sample mean length was 11.05 inches and the sample standard deviation was 0.21 inches. The technician claims that the mean rod length is more than 11 inches. 1. What type of hypothesis test should be performed?
2. What is the test statistic?
3. What is the number of degrees of freedom?
4. Does sufficient evidence exist at the α=0.01 significance level to support the technician's claim?

H0 : μ = 11

H0 : μ > 11 ;

Test statistic = 1.506

Degree of freedom = 39

There isn't sufficient evidence to conclude that mean length of rod is greater than 11.05 inches

Explanation:

Given :

Mean length, μ = 11

Sample Standard deviation, s = 0.21

Sample mean, xbar = 11.05

Sample size, n = 40

The hypothesis :

H0 : μ = 11

H0 : μ > 11

The test statistic :

This a one sample t test :

Hence, test statistic would be :

T = (xbar - μ) ÷ (s/√(n))

T = (11.05 - 11) ÷ (0.21/√(40))

T = 0.05 / 0.0332039

T = 1.506

The degree of freedom ; df ;

df = n - 1 ; df = 40 - 1 = 39

The Critical value ;

Tcritical(0.01, 39) = 2.426

Decision region :

Reject H0 if Test statistic > TCritical

Since 1.506 < 2.426 ; WE fail to reject H0 and conclude that there isn't sufficient evidence to conclude that mean length of rod is greater than 11.05 inches

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