Question

1.) Resistors are electronic components that limit the flow of electrons through a circuit. The electrical resistance of a resistor is measured in Ohms. A certain type of resistor is advertised to have an average resistance of 100 Ohms. A sample of 20 resistors is selected and gives a mean resistance of 102.4 Ohms and sample standard deviation of ? = 5.1 Ohms. Assuming resistance is Normally distributed, is there evidence to suggest the average resistance of this type of resistor is not 100 Ohms. Answer this question by performing the appropriate hypothesis test using an alpha-level of 0.05.

Answer 1

Given: = 100, = 102.4, s = 5.1, n = 20, = 0.05

The Hypothesis:

H0: = 100

Ha: 100

This is a 2 tailed test

The Test Statistic: Since the population standard deviation is unknown, we use the students t test.

The test statistic is given by the equation:

t observed = 2.11

The p Value: The p value for t = 2.11, for degrees of freedom (df) = n-1 = 19, is; p value = 0.0483

The Critical Value:   The critical value (2 Tail) at = 0.05, for df = 19, t critical= +2.093 and -2.093

The Decision Rule:   If t observed is > t critical or If t observed is < -t critical, Then reject H0.

Also if P value is < , Then Reject H0.

The Decision:   Since t observed (2.11) is > t critical (2.093), We Reject H0.

Also since P value (0.0483) is < (0.05) , We Reject H0.

The Conclusion: There is sufficient evidence at the 95% significance level to conclude that the resistance of this type of resistor is not 100 Ohms.