A bass is a kind of fish that lives mostly in lakes or rivers. Adult bass in a n

Question

A bass is a kind of fish that lives mostly in lakes or rivers. Adult bass in a nearby lake named Silver Lake have an average length of 12.3 inches with a standard deviation of 3 inches. Recently, fishermen in Silver Lake told a reporter that this year they have been catching adult bass that are smaller than usual. A research group interested in the size of the fish took a random sample of 100 adult bass from Silver Lake. The researchers found that the mean length of the bass in the sample was 11.2 inches. Which of the following is the most appropriate statistical conclusion about the difference of 1.1 inches between the sample mean of 11.2 inches and the population mean of 12.3 inches?

Explanation / Answer

The statistical software output for this problem is:

One sample Z hypothesis test:
: Mean of population
H0 : = 12.3
HA : < 12.3
Standard deviation = 3

Hypothesis test results:

So,

We can see that the p - value is very small and hence, we reject Ho. Therefore,

We can say that the difference of 1.1 inches between the sample mean of 11.2 inches and the population mean of 12.3 inches is statistically significant and we can conclude that this year fishermen have been catching adult bass that are smaller than usual.

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