On a can of sardines it is written that the can contains 10 sardines. You open up 100 cans and find the average is 9.75 sardines with a standard deviation of 1. What is the test statistic in a test of the null hypothesis that the population average is 10? Can you reject the null at the 5% significance level?

The test statistic is -2.5

Yes, I can reject the null hypothesis at 5% significance level.

Step-by-step explanation:

Null hypothesis: The average number of sardines in a can is 9.75

Alternate hypothesis: The average number of sardines in a can is greater than 9.75

Test statistic (z) = (sample mean - population mean) ÷ sd/√n

sample mean = 9.75

population mean = 10

sd = 1

n = 100

z = (9.75 - 10) ÷ 1/√100 = -0.25 ÷ 0.1 = -2.5

The test is a one-tailed test. At 5% significance level, the critical value is 1.645

Conclusion:

Reject the null hypothesis because the test statistic -2.5 is less than the critical value 1.645