Study text: "Essential Mathematics and Statistics for Science", 2nd Edition,

G Currell & A A Dowman, Wiley-Blackwell, 2009

G Currell & A A Dowman, Wiley-Blackwell, 2009

- Five replicate measurements of blood-alcohol level are made of the same sample of blood, giving values (in mg per 100 mL) of:

Use a one-sample, 1-tailed,81.8 82.9 84.4 78.8 82.5 *t*-test to decide, at a signficance level of 0.05, whether the blood-alcohol level,*µ*, in the sample is greater than 80 mg per 100 mL.

Which ONE of the following results is correct? (Download Excel data file)- You calculate
*p*= 0.044, and cannot accept that*µ*> 80 mg per 100 mL - You calculate
*p*= 0.088, and cannot accept that*µ*> 80 mg per 100 mL - You calculate
*p*= 0.044, and accept that*µ*> 80 mg per 100 mL - You calculate
*p*= 0.088, and accept that*µ*> 80 mg per 100 mL

- You calculate
- Five replicate measurements of the refractive index of broken glass at a crime scene gives values:

Replicate measurements of the glass on a suspect’s clothing have refractive indices:1.536394 1.536408 1.536368 1.536365 1.536307

The suspect’s defence claims that glass on the clothing has a1.536418 1.536434 1.536469 **different**refractive index from that at the crime scene.

Use a two-sample, 2-tailed,*t*-test to decide whether, at a significance level of 0.05, the refractive indices are different. Assume that the population variance would be the same for both sets of measurements.

Which ONE of the following results is correct? (Download Excel data file)- You calculate
*p*= 0.031, and accept that the claim is correct - You calculate
*p*= 0.021, and accept that the claim is correct - You calculate
*p*= 0.015, and accept that the claim is correct - None of the above.

- You calculate
- You are testing whether an increase in temperature changes the yield of a given chemical process.

You repeat the experiment four times at both 80C and 90C, giving the results:

Use a two-sample*T*= 90 C71.8 69.3 75.6 72.8 *T*= 80 C75.5 77.8 74.5 80.7 *t*-test to decide whether, at a significance level of 0.05, there is a difference in the yield with the increase in temperature. Assume that the population variance would be the same for both sets of measurements.

Which ONE of the following results is correct? (Download Excel data file)- You use a 1-tailed test to give
*p*= 0.023, and conclude that there is a difference. - You use a 1-tailed test to give
*p*= 0.019, and conclude that there is a difference. - You use a 2-tailed test to give
*p*= 0.046, and conclude that there is a difference. - You use a 2-tailed test to give
*p*= 0.038, and conclude that there is a difference.

- You use a 1-tailed test to give
- Five students, A, B, C, D and E, use five different pH meters to measure the pH of solution X, and obtain the values:

The variation in the result is partly due to random variation and partly due to systematic errors in the calibration of each of the pH meters.A: 8.16 B: 8.10 C: 8.15 D: 8.09 E: 8.24

The students then measure, without re-calibrating the pH meters, the pH of solution Y, and obtain the values:

The aim is to test whether there is a difference in the pH of the two solutions, assuming a signficance level of 0.05.A: 8.20 B: 8.14 C: 8.15 D: 8.15 E: 8.28

Which ONE of the following analyses is correct? (Download Excel data file)- A 1-tailed, two sample
*t*-test, assuming equal variance, to give*p*= 0.182, which does not imply that there is a difference. - A 2-tailed, two sample
*t*-test, assuming equal variance, to give*p*= 0.364, which does not imply any difference. - A 2-tailed, paired
*t*-test gives*p*= 0.021, which does imply that there is a difference. - None of the above

- A 1-tailed, two sample
- A student makes four replicate measurements of the lead concentration in each of two solutions, X and Y. The experimental results (in ppm) for each solution are given in the table below:

Mean of X values = 45.4 ppm and mean of Y values = 44.2 ppm.X 45.9 45.4 45.9 44.4 Y 45.4 44.3 43.8 43.3

Assuming a significance level of 0.05, which ONE of the following analyses would be correct for a comparison of the two solutions? (Download Excel data file)- The student performs a 2-tailed, two sample,
*t*-test, to give*p*= 0.065, and is unable to identify a difference between the lead concentrations in X and Y. - The student performs a 2-tailed, two sample,
*t*-test, to give*p*= 0.081, and is unable to identify a difference between the lead concentrations in X and Y. - Seeing that the mean of X appears to be greater than the mean of Y, the student performs a 1-tailed, two sample,
*t*-test, to give*p*= 0.018, and then concludes that the concentration in X is greater than in Y. - Seeing that the mean of X appears to be greater than the mean of Y, the student performs a 1-tailed, two sample,
*t*-test, to give*p*= 0.040, and then concludes that the concentration in X is greater than in Y.

- The student performs a 2-tailed, two sample,