Question

In: Statistics and Probability

a bait and tackle shop claims that the average trout caught in a nearby lake weighs...

a bait and tackle shop claims that the average trout caught in a nearby lake weighs 21 ounces with a standard deviation of 2.9 ounces. A random sample of 60 trout has a mean weight of 20.8 ounces. does the population differ significantly at the 0.05 level of significance?

Expert Solution

Solution :

Given that,

Population mean = = 21

Sample mean = = 20.8

Population standard deviation = = 2.9

Sample size = n = 60

Level of significance = = 0.05

This is a two tailed test.

The null and alternative hypothesis is,

Ho: 21

Ha: 21

The test statistics,

Z = ( - )/ (/)

= ( 20.8 - 21 ) / ( 2.9 / 60)

= -0.53

P-value = 2*P(Z < z)

= 2*P(Z < -0.53)

= 2*0.2981

= 0.5962

The p-value is p = 0.5962 , and since p = 0.5962 ≥ 0.05, it is concluded that the null hypothesis is fail to reject.

Conclusion:

It is concluded that the null hypothesis Ho is fail to reject. Therefore, there is not enough evidence to claim that the population mean μ is different than 21, at the 0.05 significance level.

orchestra answered 2 years ago

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