It is known that 78% of patients recover from a disease without treatment. In a trial, 100 patients take a new drug and 85 recover. Jacob believes this provides evidence that the drug is effective...

Party Z received 36% of the vote in the last general election. In a recent survey of 80 people, 25 indicated they would vote for Party Z. Does this provide evidence that support for the party has changed?

Gavin has a six-sided die. He believes it shows more 5s than it should.

Blood testosterone levels are normally distributed with mean 24nmol/L and standard deviation 6nmol/L.

A sprinter gives two samples after a race with an average blood testosterone level of 34nmol/L. Does this provide evidence that their testosterone level is above the mean?

The national mean score in Mathematics GCSE was 4.73 with standard deviation 1.21. A sample of 50 students from a particular school had mean 4.81.

i) State two assumptions necessary to carry out a hypothesis test to see if the mean was higher in this school.

The national mean score in Mathematics GCSE was 4.73 with standard deviation 1.21. In a sample of 50 students from a particular school had mean 4.81.

ii) State the hypotheses in a test to see if the mean was higher in this school.

The correlation coefficient between the mass and height of students in a sample of six students was 0.85.

State the hypotheses for a test of whether mass and height are positively correlated.

The correlation coefficient between the amount of water used in a town and the temperature over a 30-day period is 0.85.

Jane thinks there is a correlation between water used and temperature. State the null and alternative hypotheses she should use to test her suspicion.