Oxygen demand is a term biologists use to describe the oxygen needed by fish and other aquatic organisms for survival. The Environmental Protection Agency conducted a study of a wetland area. In this wetland environment, the mean oxygen demand was μ = 9.8 mg/L with 95% of the data ranging from 6.0 mg/L to 13.6 mg/L. Let x be a random variable that represents oxygen demand in this wetland environment. Assume x has a probability distribution that is approximately normal. (a) Use the 95% data range to estimate the standard deviation for oxygen demand. (b) An oxygen demand below 8 indicates that some organisms in the wetland environment may be dying. What is the probability that the oxygen demand will fall below 8 mg/L? (Round your answer to four decimal places.) (c) A high oxygen demand can also indicate trouble. An oxygen demand above 12 may indicate an overabundance of organisms that endanger some types of plant life. What is the probability that the oxygen demand will exceed 12 mg/L? (Round your answer to four decimal places.)

In a survey of 145 students at GCSC it was found that 47 of them were enrolled in the course Mathematics for the Liberal Arts. If two students from this survey were randomly chosen without replacement, what is the probability at least one of them is enrolled in the courseMathematics for the Liberal Arts?

Round your answer to 4 decimal places.

(Hint: The complement of "at least one" is "none". Find the probability that neither of the two people chosen is enrolled in the course and then use the "complements principle" to find your answer.)

An outbreak of Salmonella-related illness was attributed to ice cream produced at a certain factory. Scientists are interested to know whether the mean level of Salmonella in the ice cream is greater than 0.2 MPN/g. A random sample of 20 batches of ice cream was selected and the level of Salmonella measured.   The levels (in MPN/g) were:

1. (0.5 point) Read the data in R using a vector. Show your codes only but not the output.

2. (0.5 point) State the two hypotheses of interest.

3. (1 point) Is there evidence that the mean level of Salmonella in the ice cream is greater than 0.2 MPN/g? Assume a Normal distribution and use α = 0.05. Show your codes and result/output from R.

4. (1 point) Interpret your finding in (c).

The efficieny expert investigating the pit stop completion times collected information from a sample of n = 50 trial run pit stops and found the average time taken for these trials is 10.75 secs and that the times varied by a standard deviation of s = 2.5 secs.
Help the efficiency expert to test whether this shows evidence that the pit crew are completing the change in less than 12 secs, testing the hypotheses you selected in the previous question.
Complete the test by filling in the blanks in the following:

• An estimate of the population mean is .
• The standard error is .
• The distribution is  (examples: normal / t12 / chisquare4 / F5,6).

The test statistic has value TS=  .
Testing at significance level α = 0.05, the rejection region is:
(less/greater) than  (2 dec places).
Since the test statistic  (is in/is not in) the rejection region, there (is evidence/is no evidence) to reject the null hypothesis, H ₀.
There (is sufficient/is insufficient) evidence to suggest that the average time taken for the pit crew to complete the pit stop, μ, is less than 12 .

Were any assumptions required in order for this inference to be valid?
a: No - the Central Limit Theorem applies, which states the sampling distribution is normal for any population distribution.
b: Yes - the population distribution must be normally distributed.
Insert your choice (a or b):

The test statistic has value TS=  .
Testing at significance level α = 0.05, the rejection region is:
(less/greater) than  (2 dec places).
Since the test statistic  (is in/is not in) the rejection region, there (is evidence/is no evidence) to reject the null hypothesis, H ₀.

A sample standard deviation and sample size are given. Use the one-standard-deviation χ2-interval procedure to obtain the specified confidence interval. s = 4, n = 11 , 95% confidence interval a) 2.795 to 3.51 b) 0.618 to 3.896 c) 2.956 to 6.373 d) 2.795 to 7.02

In a sequence of independent flips of a fair coin, let N denote the number of flips until there is a run of three consecutive heads. Find P(N ≤ 8). (Should write out transition matrix.)

In 2012 the General Social Survey asked 840 adults how many years of education they had. The sample mean was 8.11 years with a standard deviation of 8.91 years.

An 80% interval for the mean number of years of education. Round the answers to two decimal places.

An 80% confidence interval for the mean number of years of education is _< μ <_.

Stephan makes 19 out of 25 foul shots. Use the normal distribution in probability and confidence interval calculations.

1. a) What is the a value for a confidence level of 80%?

2. b) What is the standard deviation of the sample proportion x/n where x is the number

   of made shots and n is the total number of shots?

3. c) What is the 80% confidence interval for underlying average foul shot percentage?

The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to detect the moths. When traps are checked periodically, the mean number of moths trapped is only 0.5, but some traps have several moths. The distribution of moth counts is discrete and strongly skewed, with standard deviation 0.7.

(a) What are the mean and standard deviation of the average number of moths x⎯⎯⎯x¯ in 65 traps?
(b) Use the central limit theorem to find the probability that the average number of moths in 65 traps is greater than 0.4.

Suppose the people living in a city have a mean score of

5454

and a standard deviation of

1010

on a measure of concern about the environment. Assume that these concern scores are normally distributed. Using the

​50%minus−​34%minus−​14%

​figures, approximately what percentage of people have a score​ (a) above

5454​,

​(b) above

6464​,

​(c) above

3434​,

​(d) above

4444​,

​(e) below

5454​,

​(f) below

6464​,

​(g) below

3434​,

and​ (h) below

4444​?

1.

2.

3.

4.

The null and alternate hypotheses are: H0 : μd ≤ 0 H1 : μd > 0 The following sample information shows the number of defective units produced on the day shift and the afternoon shift for a sample of four days last month. Day 1 2 3 4 Day shift 10 11 14 18 Afternoon shift 8 11 12 15 At the 0.100 significance level, can we conclude there are more defects produced on the day shift? Hint: For the calculations, assume the day shift as the first sample. State the decision rule. (Round your answer to 2 decimal places.) Compute the value of the test statistic. (Round your answer to 3 decimal places.) What is the p-value? Between 0.025 and 0.05 Between 0.001 and 0.005 Between 0.005 and 0.01 What is your decision regarding H0? Reject H0 Do not reject H0

A physicist examines 4 seawater samples for potassium chloride concentration. The mean potassium chloride concentration for the sample data is 0.604 cc/cubic meter with a standard deviation of 0.0177. Determine the 80% confidence interval for the population mean potassium chloride concentration. Assume the population is approximately normal.

1)Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

2)Construct the 80% confidence interval. Round your answer to three decimal places.