11 In 2010 the heights of adult women in the UK were found to have mean \(\mu = 161.6 \mathrm {~cm}\) and variance \(\sigma ^ { 2 } = 1.96 \mathrm {~cm} ^ { 2 }\).
It is believed that the mean height of adult women in 2020 in the UK is greater than in 2010.
In 2020 a researcher collected a random sample of the heights of 200 adult women in the UK.
The researcher calculated the sample mean height and carried out a hypothesis test at the \(5 \%\) level to investigate whether there was any evidence to suggest that the mean height of adult women in the UK had increased.
The researcher assumed that the variance was unaltered.
- - State suitable hypotheses for the test, defining any variables you use.
- Explain whether the researcher conducted a 1-tail or a 2-tail test.
- Determine the critical region for the test.
The researcher found that the sample mean was 161.9 cm and made the following statements.
- The sample mean is in the critical region.
- The null hypothesis is accepted.
- This proves that the mean height of adult women in the UK is unaltered at 161.6 cm .
- Explain whether each of these statements is correct.