DP Mathematics: Applications and Interpretation Questionbank

Suggest, with justification, a valid conclusion that Talha could make.

Find an unbiased estimate for the mean number $\left(\mu \right)$ of chocolates per packet.

Use the formula $s_{n-1}^2=\frac{\text{Σ}{x}^2-{\displaystyle \frac{{\left(\text{Σ}x\right)}^2}{n}}}{n-1}$ to determine an unbiased estimate for the variance of the number of chocolates per packet.

Find a $95\%$ confidence interval for $\mu$. You may assume that all conditions for a confidence interval have been met.

Find $s_{n-1}$ for this sample.

Find a 95 % confidence interval for the population mean, giving your answer to 4 significant figures.

The bags are labelled as being 1.5 kg mass. Comment on this claim with reference to your answer in part (b).

State suitable hypotheses for a two-tailed test.

Find the critical region for testing $\overline{b}$ at the 5 % significance level.

Find the probability of making a Type II error.

Another model of smartphone whose battery life may be assumed to be normally distributed with mean μ hours and standard deviation 1.2 hours is tested. A researcher measures the battery life of six of these smartphones and calculates a confidence interval of [10.2, 11.4] for μ.

Calculate the confidence level of this interval.

Find unbiased estimates of the mean of $T$.

Find unbiased estimates of the variance of $T$.

Assuming that $T$ is normally distributed, find

(i)  the 90% confidence interval for the mean time taken to travel to work by the workers of this company,

(ii)  the 95% confidence interval for the mean time taken to travel to work by the workers of this company.

Before seeing these results the managing director believed that the mean time was 26 minutes.

Explain whether your answers to part (b) support her belief.

State the distribution of $\overline{X}$ giving its mean and variance.

Find an unbiased estimate for $\mu$.

Find an unbiased estimate for ${\sigma }^2$.

Find a 90 % confidence interval for $\mu$.

Find the $p$-value for the test.

Write down the conclusion reached.

Jack takes a random sample of size 100 and calculates that $\overline{x}=60.2$. Find an approximate 90 % confidence interval for $\mu$.