Question

An ornithologist believes that there is a relationship between the tail length, t mm, and the wing length, w mm, of female hook-billed kites. A random sample of size 10 is taken from a database of these kites and the relevant data is given in the table below. | t (mm) | 191 | 197 | 208 | 180 | 188 | 210 | 196 | 191 | 179 | 208 | | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | | w (mm) | 284 | 285 | 288 | 273 | 280 | 283 | 288 | 271 | 257 | 289 | The ornithologist plans to use a linear regression model based on these data and interpolate or extrapolate as necessary to estimate the wing length of other female hook-billed kites from their tail length. (a) (i) Explain what is meant by extrapolation. (1) (ii) Explain the dangers of extrapolation. (1) The ornithologist attempts to calculate the product moment correlation coefficient, r, and obtains a value of 1.3. (b) Explain how she should be able to identify that this is incorrect without carrying out any further calculations. (1) (c) Use your calculator to find the correct value of the product moment correlation coefficient, r. (1) (d) Stating your hypotheses clearly test, at the 1% significance level, whether there is evidence that the product moment correlation coefficient for the population is positive. (3) (e) Explain what your test in part (d) suggests about female hook-billed kites. (1)

          An ornithologist believes that there is a relationship between the tail length, t mm, and the wing length, w mm, of female hook-billed kites. A random sample of size 10 is taken from a database of these kites and the relevant data is given in the table below.

| t (mm) | 191 | 197 | 208 | 180 | 188 | 210 | 196 | 191 | 179 | 208 |
| :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- |
| w (mm) | 284 | 285 | 288 | 273 | 280 | 283 | 288 | 271 | 257 | 289 |

The ornithologist plans to use a linear regression model based on these data and interpolate or extrapolate as necessary to estimate the wing length of other female hook-billed kites from their tail length.

(a) (i) Explain what is meant by extrapolation. (1)
(ii) Explain the dangers of extrapolation. (1)

The ornithologist attempts to calculate the product moment correlation coefficient, r, and obtains a value of 1.3.

(b) Explain how she should be able to identify that this is incorrect without carrying out any further calculations. (1)

(c) Use your calculator to find the correct value of the product moment correlation coefficient, r. (1)

(d) Stating your hypotheses clearly test, at the 1% significance level, whether there is evidence that the product moment correlation coefficient for the population is positive. (3)

(e) Explain what your test in part (d) suggests about female hook-billed kites. (1)

An ornithologist believes that there is a relationship between the tail length, t mm, and the wing length, w mm, of female hook-billed kites. A random sample of size 10 is taken from a database of these kites and the relevant data is given in the table below.

| t (mm) | 191 | 197 | 208 | 180 | 188 | 210 | 196 | 191 | 179 | 208 |
| :— | :— | :— | :— | :— | :— | :— | :— | :— | :— | :— |
| w (mm) | 284 | 285 | 288 | 273 | 280 | 283 | 288 | 271 | 257 | 289 |

The ornithologist plans to use a linear regression model based on these data and interpolate or extrapolate as necessary to estimate the wing length of other female hook-billed kites from their tail length.

(a) (i) Explain what is meant by extrapolation. (1)
(ii) Explain the dangers of extrapolation. (1)

The ornithologist attempts to calculate the product moment correlation coefficient, r, and obtains a value of 1.3.

(b) Explain how she should be able to identify that this is incorrect without carrying out any further calculations. (1)

(c) Use your calculator to find the correct value of the product moment correlation coefficient, r. (1)

(d) Stating your hypotheses clearly test, at the 1% significance level, whether there is evidence that the product moment correlation coefficient for the population is positive. (3)

(e) Explain what your test in part (d) suggests about female hook-billed kites. (1)

Added by Kevin C.

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