Statistics and Probability Answers

Student Q.T. M.A

Ranking Ranking

A 2 3

B 7 6

C 6 4

D 1 2

E 4 5

F 3 1

G 5 8

H 8 7

Work out the spearman rank correlation .

A study by consumer Exports showed that 64% of supermarket shoppers believe supermarket brands to be as good as national name brands. To investigate whether this results applies to its own product, the manufacturer of a national name brand Ketch up asked a sample of shoppers whether they believe that super markets Ketchup was as good as the national brand Ketchup.

a. Formulate the hypotheses that could be used to determine whether the percentage of supermarket shoppers who believe that the supermarket Ketchup was as good as the national brand Ketchup differed from 64%.

b. If a sample of 100 shoppers showed 52 stating that the supermarket brand was as good as the national brand what is the P-value?

c. At ∝ = 0.05, what is your conclusion?

d. Should the national brand Ketchup manufacturer be pleased with this conclusion? Explain.

A website has on the average two hits per hour. Assuming a Poisson distribution for the number of hits per hour (X), calculate the probability that there are at most three hits.

Evaluate #2 and #3 in light of #1 being true.

1.It's been reported that the mean height for an American female is 64 inches with a standard deviation of 3 inches.
2. Since the mean height equals the median height and the interquartile range = 1.3 standard deviations, we can safely assume the data normally distributed.
3. Therefore, the percentage of women greater than 72 inches would be less than ½%.

When a newspaper or magazine article reports the results of a study and draws a conclusion without also reporting whether the results are statistically significant, what are the possible reasons for doing so? How seriously should you take the conclusion offered in such a study? Discuss.

A manufacturer of automobile seats has a production line that produces an average of
100 seats per day. Because of new government regulations, a new safety device has
been installed, which the manufacturer believes will reduce average daily output. A
random sample of 15 days output after the installation of the safety device is shown:
93, 103, 95, 101, 91, 105, 96, 94, 101, 88, 98, 94, 101, 92, 95 .
Assuming that the daily output is normally distributed, is there sufficient evidence to
conclude that average daily output has decreased following the installation of the
safety device? (Use α = 0.05 )

Consider a small post office with a single staff member operating a single postal
counter. Suppose that the probability pk, that there are k customers in the post
office, is given by pk = p0p^k k = 0,1,2,... where 0 < p < 1.
(a) Show that p0 = 1 - p.
(b) Determine the probability that a newly arriving customer has to wait to be
served.

A simple random sample of 36 cans of regular Coke has a mean volume of 12.19 oz. Assume that the standard deviation of all cans of regular Coke is 0.11 oz. Use a 0.01 significance level to test the claim that cans of regular Coke have volumes with a mean of 12 oz, as stated on the label.

a. State the null (H0) and alternative (H1) hypotheses.

Find the values of the 30th and 90th percentiles of the data. Please show your work.
129, 113, 200, 100, 105, 132, 100, 176, 146, 152

The genetic features of a group of adult mice are such that the probability of an offspring
being albino is 0.2. If 50 offsprings are born to a group of such mice, find the probability that
15 or more of them are albinos.