Write down the null and alternative hypotheses for each of the following situations: The average IQ in a school ($\mu $) over a long period of time has been $102$. It is thought that changing the mathematics teacher might influence the average IQ. It is claimed that the average size of $5$ minutes long video created by a camera ($\mu $) is $712$ Mb. A computer engineer believes that this figure is inaccurate. A consumer believes that chicken nuggets sold in packets of $1$ kg are on average underweight. A student believes that the average extra amount earned by degree holders is more than $\$3000$/month. The mean braking force of a cable does not normally exceed $5000$N. A new brand claims that it regularly does exceed this value. The average time taken to match a fingerprint on a smartphone is normally more than $0.72$ seconds. A new phone claims to be able to do better. The fraction of apple flavoured toffees in a box if advertised as being $20\%$ but Milo thinks that it is more than this. The standard deviation of measurements of the temperature of meat is thought to have decreased from its previous value of $0.5{}^\circ \text{C}$.

Null and Alternative Hypotheses

Write down the null and alternative hypotheses for each of the following situations:

The average IQ in a school ($\mu $) over a long period of time has been $102$. It is thought that changing the mathematics teacher might influence the average IQ.
It is claimed that the average size of $5$ minutes long video created by a camera ($\mu $) is $712$ Mb. A computer engineer believes that this figure is inaccurate.
A consumer believes that chicken nuggets sold in packets of $1$ kg are on average underweight.
A student believes that the average extra amount earned by degree holders is more than $\$3000$/month.
The mean braking force of a cable does not normally exceed $5000$N. A new brand claims that it regularly does exceed this value.
The average time taken to match a fingerprint on a smartphone is normally more than $0.72$ seconds. A new phone claims to be able to do better.
The fraction of apple flavoured toffees in a box if advertised as being $20\%$ but Milo thinks that it is more than this.
The standard deviation of measurements of the temperature of meat is thought to have decreased from its previous value of $0.5{}^\circ \text{C}$.

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