Question

A company that produces fishing line undergoes random testing to see if their fishing line holds up to the advertised specifications. Currently they are producing 30-pound test line and 20 randomly selected pieces are selected to test the strength. The 20 pieces broke with an average force of 29.1 pounds and a sample standard deviation of 2 pounds. Assuming that the strength of the fishing line is normally distributed, perform the appropriate hypothesis test at a 0.05 significance level in order to determine whether there is sufficient sample evidence to conclude the fishing line breaks with an average force of less than 30 pounds.

how would you figure out on a TI84?

Answer 1

Solution:

Given:

Sample size = n = 20

Sample mean =

Sample standard deviation = s = 2

the strength of the fishing line is normally distributed.

Level of significance =

We have to test if there is sufficient sample evidence to conclude the fishing line breaks with an average force of less than 30 pounds.

Thus this is left tailed test.Thus we use following steps:

Step 1) State H0 and H1:

Vs

Step 2) Find Test statistic value.

Since sample size n = 20 is small and population standard deviation is unknown we use one sample t test for mean.

We use following steps in TI 84:

1) Press STAT and Select TESTS

2) Under TESTS select T-Test

3) Under T-Test , select Stats

4) Under Enter Numbers:

Click on Calculate and press Enter

We get:

t test statistic value = -2.012

Step 3) Find p-value:

From above TI84 output, we get:

p-value = p = 0.02928 = 0.0293

Step 4) Decision Rule:

Reject H0, if p-value < 0.05 level of significance, otherwise we fail to reject H0.

Since p-value= 0.0293 < 0.05 level of significance, we reject H0.

Step 5) Conclusion:

Since we have rejected null hypothesis H0, there is sufficient sample evidence to conclude the fishing line breaks with an average force of less than 30 pounds.