Two-sample t-tests Problem set B

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 heights of plants given fertiliser X (9 plants) and fertiliser Y (11 plants).
2. (b) Test whether the mean waiting time at a clinic differs from the stated 15 minutes, using 25 patients.
3. (c) Compare the mean scores of two classes, with 22 and 19 students.

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

1. (a) Does the mean daily step count differ between office workers (group 1) and teachers (group 2)?
2. (b) A baker thinks loaves made with flour A (group 1) have a lower mean mass than loaves made with flour B (group 2).

Two brands of battery are timed while charging. The charging times, in hours, are summarised. Test, at the 5% significance level, whether the mean charging time of brand 1 is less than that of brand 2. Assume the times are normally distributed with equal variance. State the hypotheses, then find t and p and say whether H0 is rejected.

The hours of sleep per night of random samples of students at two schools are summarised. Test, at the 5% significance level, whether the mean hours of sleep differ between the schools. Assume the hours are normally distributed with equal variance. State the hypotheses, then find t and p and say whether H0 is rejected.

The heights, in cm, of 7 seedlings grown under light 1 and 6 seedlings grown under light 2 are recorded. Test, at the 5% significance level, whether the mean height under light 1 is greater than under light 2. Assume the heights are normally distributed with equal variance. State the hypotheses, then find t and p and say whether H0 is rejected.

A coach gives one group of athletes training plan A (group 1) and another group plan B (group 2). The numbers of press-ups each athlete can do in one minute are summarised. The coach thinks plan A gives a higher mean. 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 daily screen time, in hours, of random samples of students in Year 10 and Year 12 is summarised. Test, at the 1% significance level, whether the mean daily screen time differs between the year groups. Assume the times 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 life of two models of phone battery differs gives a p-value of 0.043.

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

An angler compares the masses, in kg, of 7 fish caught with bait A (group 1) and 8 fish caught with bait B (group 2). She believes bait A catches heavier fish on average.

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 cycling club compares the distance, in km, ridden before a puncture with a new tyre (group 1, 14 tyres) and a standard tyre (group 2, 17 tyres). The club thinks the new tyre lasts longer. 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.