A random sample of 64 bags of white cheddar popcorn weighted, on average 5.23 ounces with a standard deviation of 0.24 ounce. We want to test whether the population mean weight of white cheddar bag is different than 5.5 ounces. Use = 0.05.

a) State the assumptions

b) State null and alternative hypotheses.

c) Write down the formula of test statistic. State the distribution of test statistic if the null hypothesis is true. Calculate the value of test statistic.

d) Use R to find P-value. Interpret the p-value in context of the problem.

e) Make a decision (whether to reject the null or not) and draw a conclusion in context of the problem.

Based on your conclusion from the previous question, which of the following is the correct 95% confidence interval of , average weight of such kind of popcorn. Explain. No calculation required.

(A) (5.1, 5.2)

(B) (4.7, 5.7)

(C) (5.2, 5.6)