Question

IST analyzes the fish population of coastal alaska waters. each year they sample 100 fish and measure their weight. the table shows the mean fish weights for 2016, 2017, 2018. Assume a population standard deviation of 5lb. alpha = .05

Year. Mean salmon weight lb

2016: 18

2017: 19

2018: 23

A.) is the increase from 2016 to 2017 statistically significant. state test statistic and p-value, then answer the question.

B) is the increase from 2017 to 2018 statistically significant. state test statistic and p-value, then answer the question.

C) is the increase from 2016 to 2018 statistically significant. state test statistic and p value, then answer the question.

Answer 1

We use z test as standard deviation is given and sample size is large enough

As the standard deviation of i same for all and we are looking for the difference in mean weights for two years at a time so the standard error of the sampling distribution of difference of means is

a) The value of the test static is

The test is right tailed as we are looking for increase

So P-value is

As 0.0793> 0.05

We fail to reject the null hypothesis

There is not enough evidence to support the claim that mean weight has increased from 2016 to 2017

b)

The value of the test static is

The test is right tailed as we are looking for increase

So P-value is

As 0< 0.05

We reject the null hypothesis

There is enough evidence to support the claim that mean weight has increased from 2017 to 2018

c)

The value of the test static is

The test is right tailed as we are looking for increase

So P-value is

As 0< 0.05

We reject the null hypothesis

There is enough evidence to support the claim that mean weight has increased from 2016 to 2018