Determine the sample space for the following experiments. (a) A student is selected at random and his GPA is recorded. (b) A player chooses two cards at random from a standard deck of cards and records their sum. (Assume face cards have a value of 10 and aces can take a value of 1 or 11, as in black jack.) (c) Choose an odd number from 1 to 13 at random.
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1. Determine the
(a) A student is selected at random and his GPA is recorded.
(b) A player chooses two cards at random from a standard deck of cards and records
their sum. (Assume face cards have a value of 10 and aces can take a value of 1
or 11, as in black jack.)
(c) Choose an odd number from 1 to 13 at random.
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- Suppose you are interested in buying a new Lincoln Navigator or Town Car. You are standing on the sales lot looking at a model with different options. The list price is on the vehicle. As a salesperson approaches, you wonder what the dealer invoice price is for this model with its options. The following data are based on a random selection of these cars of different models and options. Let y be the dealer invoice (in thousands of dollars) for the given vehicle. x 32.4 32.9 36.1 44.0 47.8 y 30.4 31.0 32.0 42.1 42.2 (b) Use a 10% level of significance to test the claim that ρ > 0. (Use 2 decimal places.) t ? critical t ? (c) Verify that Se ≈ 1.5629, a ≈ 2.5006, and b ≈ 0.8551. Se ? a ? b ? (e) Find a 95% confidence interval for y when x = 42 (thousand dollars). (Use 2 decimal place.) lower limit ? upper limit ? (f) Use a 10% level of significance to test the claim that β > 0. (Use 2 decimal places.) t ? critical t ?Suppose that Mairin has knit a collection of wool‑blend infinity scarves that she wants to sell in her Etsy shop for $28.00 each. However, she is worried that if the average price of comparable scarves is less than $28.00, hers would be less likely to sell. Mairin selected a random sample of 9 similar hand‑knit, wool‑blend infinity scarves, and their prices are as follows. $21.75,$24.00,$27.25,$29.95,$23.00,$26.00,$27.80,$33.50,$27.00$21.75,$24.00,$27.25,$29.95,$23.00,$26.00,$27.80,$33.50,$27.00 Use a left‑tailed one‑sample ?t‑test to determine whether the average price of hand‑knit, wool‑blend infinity scarves sold on Etsy is less than $28.00. Assume that the prices of all comparable scarves are normally distributed. Mairin should (reject, accept, fail to accept) her null hypothesis. There is (sufficient, no, insufficient) evidence that the mean price of hand‑knit, wool‑blend infinity scarves is (greater than, different from, less than, equal two) $28.00.1. Consider the following random experiment: there is a bag with 4 marbles in it, two red and two blue. We draw two marbles from the bag, without replacement. To make the sampling uniform, let's label the two red marbles R₁ and R2 and the two blue marbles B₁ and B2. Then the sample space is {R₁R2, R₁B₁, R₁B2, R2B1, R2B2, B1B2}. Finally, let X be the indicator variable equal to 1 if the two marbles drawn have the same color, and 0 if they have different colors. (a) Write down X as a function from the sample space to the real numbers. (b) What is Rx, the range of X? (c) Write down the probability mass function Px of X: this is a function from the range of X to the interval [0, 1]. (d) Identify the distribution of X by name, and give the parameter(s) of that distribution. (The functions in parts (a) and (c) of this problem both have only finitely many possible inputs. I don't care what notation you use in your answer, as long as you give me the value of the function for every possible…
- For each of the following experiments, describe the sample space. i) Flip a coin four times ii) Flip a coin and roll a die. ii) Observe the proportion of people with blue eyes in a group of 40 people.2. In a population it is estimated that 20% have a desired trait of interest for the researcher. The researcher wants to know how many people on average he has to draw from a population to get 2 people with the trait. Use rows 20-24 of the Random Number Table to carry out the simulation. Explain clearly how you set up the problem and report your findings. Answer:. List the 10 possible samples (without replacement) of size 2 that can be obtained from the population of five officials. Lieutenant Governor (L) Secretary of State (S) Attorney General (A) Representative (R) Press Secretary (P) b. If a simple random sampling procedure is used to obtain a sample of two officials, what are the chances that it is the first sample on your list in part (a)? the secondsample? the tenth sample?
- (A5) In a certain study of 900 men from Nsawam, it was found that 25 are smokers. Use (a) Identify the population in this study. (b) What is the sample size? (c) What percentage of the sampled population are smokers? (d) State the gender of interest in the study. Men (e) What question is the researcher most likely to ask in this study? d 2 doctors An executiveR3.29. Homecoming A college statistics class conducted a survey concerning community attitudes about the college's large homecoming celebration. That survey drew its sample in the following manner: Telephone numbers were generated at random by selecting one of the local telephone exchanges (first three digits) at random and then generating a random four-digit number to follow the exchange. If a person an- swered the phone and the call was to a residence, then that person was taken to be the subject for interview. (Undergrad- uate students and those under voting age were excluded, as was anyone who could not speak English.) Calls were placed until a sample of 200 eligible respondents had been reached. | a) Did every telephone number that could occur in that community have an equal chance of being generated? b) Did this method of generating telephone numbers result in a Simple Random Sample (SRS) of local residences? Explain. c) Did this method generate an SRS of local voters? Explain.…A choral conductor has 1885 singers in her choir, some of them are professional singers. The conductor wants to estimate what percentage of singers are professional, but can't ask all 1885, so she instead asks 630 singers in front and finds 17 who are professionals. (a) Identify the sample.A. 17/1885B. 630C. singers who were askedD. None of the above. (b) Identify the populationA. percentage of entire singers who are professionalB. entire singersC. 17/1885D. None of the above. (c) What specific type of bias does this scenario demonstrate?A. Voluntary response samplingB. Convenience SamplingC. It is representative of the population.D. None of the above. (d) Identify the parameterA. range of values in which 95% values fallB. percentage of entire singers who are professionalC. 17D. None of the above.