The Nero Match Company sells matchboxes that are supposed to have an average of 40 matches per

Question:

The Nero Match Company sells matchboxes that are supposed to have an average of 40 matches per box, with σ = 9. A random sample of 94 Nero matchboxes shows the average number of matches per box to be 43.1. Using a 1% level of significance, can you say that the average number of matches per box is more than 40?
Are we testing a single mean or a single proportion? Assume underlying population distributions are mound-shaped and symmetrical for problems with small samples that involve testing a mean.
(a) What is the level of significance? State the null and alternate hypotheses.
(b) What sampling will you use? What assumptions are you making? What is the value of the sample test statistic?
(c) Find (or estimate) the P-value. Sketch the sampling and show the area corresponding to the P-value.
(d) Based on your answers in parts (a)–(c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?
(e) Interpret your conclusion in the context of the application.
Distribution
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