The mass of a standard loaf of white bread is, by law, meant to be 700 g. The Ryeband Bakery, which supplies outlets throughout the Eastern Cape, regularly checks the masses of its standard loaf of white bread. If their bread is underweight, on average, they are liable to a fine by the provincial Department of Health, whose inspectors undertake random checks; if the bread is overweight, on average, the bakery is wasting its ingredients.
On a given day, a random sample of 64 loaves is selected and weighed. The sample mean mass was found to be 695 g with a sample standard deviation of 21 g. Assume that the mass of bread is approximately normally distributed.
(a) Is Ryeband Bakery complying with provincial government regulations, while also not wasting its own resources? Formulate the null and alternative hypothesis. Conduct a hypothesis test for a single mean at the 5% level of significance. What statistical and management conclusions can be drawn?
(b) Use Excel's TDIST function to compute the p-value for the test. Interpret the findings for the Eastern Cape's provincial Department of Health.
(c) Reformulate the null and alterative hypothesis test if it is more important for the bakery to comply with government regulations (i.e. to ensure that the average mass of a standard loaf of white bread is not less than 700 g). Conduct the test at the 5% level of significance and draw the statistical and management conclusions.