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Question: Data were gathered on 159 fish from seven different species. The fish were caught in the Laengelmavesi Sea near Tampere in Finland. Various measures of length, width, and weight were obtained. We wish to focus on the perch species and the width measurements. To adjust for differences in the size of a fish due to its age, the data on the width were recorded as the percent of the length.
a) We would like to assess if the average width percent of perch from this sea is less than 16 using a 10% significance level. Let ? be the mean width percent for perch from this sea. State the corresponding hypotheses.
b) Of the 159 fish, 56 were perch. The data for the width percent are provided below. Check the assumptions for normality by creating both a histogram and a QQ plot. (Use your calculator, but copy the graphs onto your paper.) Comment on the graphs.
c) Perform the test. State the test statistic formula, its value, the p-value, your decision.
d) State your conclusion in a well written sentence.
e) Create a 90% confidence interval for these data.
Data for the 56 perch:
16 .0 0 15.7 0 14 .50 15 .9 0
1 3.6 0 14 .8 0 1 5.0 0 16 .2 0
15.20 17 .9 0 1 5.0 0 18 .1 0
15.30 15.0 0 1 5.0 0 14 .5 0
1 5.9 0 15.0 0 17 .0 0 17 .8 0
1 7 .30 15.8 0 15.10 16 . 8 0
1 6 .10 14 .3 0 15.10 17 .0 0
15.10 15.4 0 1 5.0 0 17 .6 0
14 .6 0 15 .1 0 14 .8 0 15 .6 0
13.20 17 .7 0 14 .9 0 15 .4 0
1 5.8 0 17 .5 0 14 .6 0 16 .1 0
14 .7 0 20 .9 0 1 5.0 0 16 .3 0
1 6 .30 17 .6 0 1 5.9 0 17 .7 0
15.50 17 .6 0 1 3.9 0 16 .3 0
Question: Data were gathered on 159 fish from seven different species. The fish were caught in the Laengelmavesi Sea near Tampere in Finland. Various measures of length, width, and weight were obtained. We wish to focus on the perch species and the width measurements. To adjust for differences in the size of a fish due to its age, the data on the width were recorded as the percent of the length.
a) We would like to assess if the average width percent of perch from this sea is less than 16 using a 10% significance level. Let ? be the mean width percent for perch from this sea. State the corresponding hypotheses.
b) Of the 159 fish, 56 were perch. The data for the width percent are provided below. Check the assumptions for normality by creating both a histogram and a QQ plot. (Use your calculator, but copy the graphs onto your paper.) Comment on the graphs.
c) Perform the test. State the test statistic formula, its value, the p-value, your decision.
d) State your conclusion in a well written sentence.
e) Create a 90% confidence interval for these data.
Data for the 56 perch:
16 .0 0 15.7 0 14 .50 15 .9 0
1 3.6 0 14 .8 0 1 5.0 0 16 .2 0
15.20 17 .9 0 1 5.0 0 18 .1 0
15.30 15.0 0 1 5.0 0 14 .5 0
1 5.9 0 15.0 0 17 .0 0 17 .8 0
1 7 .30 15.8 0 15.10 16 . 8 0
1 6 .10 14 .3 0 15.10 17 .0 0
15.10 15.4 0 1 5.0 0 17 .6 0
14 .6 0 15 .1 0 14 .8 0 15 .6 0
13.20 17 .7 0 14 .9 0 15 .4 0
1 5.8 0 17 .5 0 14 .6 0 16 .1 0
14 .7 0 20 .9 0 1 5.0 0 16 .3 0
1 6 .30 17 .6 0 1 5.9 0 17 .7 0
15.50 17 .6 0 1 3.9 0 16 .3 0
