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A coffee shop claims that its fresh-brewed drinks have a mean caffeine content of 80 milligrams per five ounces. You work for a city health agency and are asked to test this claim. You find that a random sample of 42 five-ounce servings has a mean caffeine content of 83 milligrams and a standard deviation of 7.5 milligrams. At = 0.05, do the evidence suggest that the mean caffeine content is in fact different than 80 milligrams per five ounces?
Explain in r code
i) null and alternative hypotheses
ii) statement of assumptions
iii) calculation of the test statistic
iv) calculation of the P-value
v) decision in terms of the null hypothesis
Find the probability density function of U + V. Let P = 2U + 3V and Q = 2U - 3V. Given that the variances of U and V are 1/4 and 1/9 respectively, show that P and Q are uncorrelated.
Is it likely that the sampling procedure created a biased sample? Discuss, including suggestions for improvement if appropriate.
a study examines self esteem and depression in children using a standardized test for depression. for the general
(a) Specify the marginal distribution of X. (b) Specify the marginal distribution of Y. (c) Are X and Y independent? Why or why not?
Investigate whether the simple genetic principle is correct by carrying out a X2 test of goodness-of-fit.
A permutation resample for a two-sample test
Assume you are in charge of a production line which allows for no more than 1% defectives in order to be in compliance. A random sample of 500 is tested and 4 defective items are found. Find the probability of getting exactly 4 defectives out of..
A store wishes to predict net profit as a function of sales for the next year. The following table gives the years 1998 to 2005.
If the code does not start with a vowel, then there must be 2 consecutive positions in the code which contain the same vowel. (For instance, both baal and blaa are acceptable codes.)
At the 0.05 level of significance, do the samples provide sufficient evidence to indicate that on the average, fewer consumers prefer a new product when the spokesperson is male?
In order to evaluate the rate of error experienced in reading chest x-rays, the following experiment is done. Several people with known tuberculosis (TB) status (through other reliable tests) are subjected to chest x-rays.
If the same price is charged for either process, what is the annual volume beyond which the automated process is more attractive?
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