Two-sample t-tests Problem set A

In each case say which t-test to use, and state the assumptions if it is a two-sample test.

1. (a) Compare the mean reaction times of 14 boys and 16 girls, chosen at random.
2. (b) Test whether the mean mass of parcels differs from the stated 2 kg, using 20 parcels.
3. (c) Compare the mean fuel use of two models of car, tested on 10 cars and 12 cars.

State the null and alternative hypotheses for each test, defining μ1 and μ2.

1. (a) Does the mean time to solve a puzzle differ between adults (group 1) and children (group 2)?
2. (b) A vet thinks dogs on diet A (group 1) lose more weight on average than dogs on diet B (group 2).

Two classes sit the same test. The marks are summarised. Test, at the 5% significance level, whether the mean mark of class 1 is greater than that of class 2. Assume the marks are normally distributed with equal variance. State the hypotheses, then find t and p and say whether H0 is rejected.

The daily sales, in pounds, of a stall at two markets are summarised. Test, at the 5% significance level, whether the mean daily sales differ between the markets. Assume the sales are normally distributed with equal variance. State the hypotheses, then find t and p and say whether H0 is rejected.

The times, in minutes, that two types of paint take to dry are recorded on 6 samples of paint 1 and 7 samples of paint 2. Test, at the 5% significance level, whether the mean drying time of paint 1 is less than that of paint 2. Assume the times are normally distributed with equal variance. State the hypotheses, then find t and p and say whether H0 is rejected.

A school teaches one group of students with a new method (group 1) and another group with the standard method (group 2). Their end-of-year marks are summarised. The school thinks the new method gives a higher mean mark. Test this belief at the 10% significance level.

1. (a) State two assumptions needed for the test.
2. (b) State the hypotheses.
3. (c) Find the t-statistic and the p-value.
4. (d) State the conclusion in context.

The weekly grocery spend, in pounds, of random samples of households in two towns is summarised. Test, at the 1% significance level, whether the mean weekly spend differs between the towns. Assume the spends are normally distributed with equal variance.

1. (a) State the hypotheses.
2. (b) Find the t-statistic and the p-value.
3. (c) State the conclusion in context.

A test of whether the mean waiting time differs between two clinics gives a p-value of 0.027.

1. (a) State the conclusion at the 5% significance level, in context.
2. (b) State the conclusion at the 1% significance level, in context.

A typing teacher compares the number of words typed per minute by 8 students who took a typing course (group 1) and 7 students who did not (group 2). She believes the course increases the mean speed.

1. (a) State two assumptions needed.
2. (b) State the hypotheses.
3. (c) Test the claim at the 5% significance level. Give t, p and the conclusion in context.

A researcher compares the memory scores of 13 students who studied with music (group 1) and 16 students who studied in silence (group 2). She thinks music improves the mean score. Test this at the 10% significance level, assuming normal populations with equal variance.

1. (a) State the hypotheses.
2. (b) Find the t-statistic and the p-value.
3. (c) State the conclusion in context.