Records show that, when all parts of the packaging process are working correctly, the amount (X) of breakfast cereal in a packet is normally distributed with mean = 700g and standard deviation = 15g.

One part of the packaging process has been adjusted, and the quality control manager thinks that, although the amount of cereal packed should still be normally distributed, with the same standard deviation (i.e. = 15g), the mean () may have changed.

The quality control manager randomly selects 27 packets of cereal and determines that the average weight of cereal for these 27 packets isx = 693.7g.

(a) Write down null and alternative hypotheses to test whether the mean amount of cereal is still 700g.

(b) Write the equation for the test statistic.

(c) What is the distribution of this test statistic if the null hypothesis is true?

(d) What is the observed value of the test statistic in this case?

(e) What is the p-value?

(f) Do you reject or retain the null hypothesis at the 5% significance level, and why?

(g) What is your conclusion?