A political poll is taken to determine the fraction p of the population that would support a referendum requiring all citizens to be fluent in the language of probability and statistics. (a) Assume p = 0.5. Use the central limit theorem to estimate the probability that in a poll of 25 people, at least 14 people support the referendum. Your answer to this problem should be a decimal. (b) With p unknown and n the number of random people polled, let Xn be the fraction of the polled people who support the referendum. What is the smallest sample size n in order to have a 90% confidence that Xn is within 0.01 of the true value of p? Your answer to this problem should be an integer.

A food company is planning to market a new kind of cereal; however before, they want to find the % of people who will like it. They select a random sample of 500 people and ask them to try the cereal. Of 500, 290 people say they like it. Compute the 95% cofidence interval for the % of the pop. that will like the cereal. Interept this cofidence interval.

Sean thinks that he has a special relationship with the number 6. In particular, Sean thinks that he would roll a 6 with a fair 6-sided die more often than you'd expect by chance alone. Suppose pis the true proportion of the time Sean will roll a 6. (a) State the null and alternative hypotheses for testing Sean's claim. (Type the symbol "p" for the population proportion, whichever symbols you need of "", "-", "not =" and express any values as a fraction e.g. p = 1/3) Ho= Ha (b) Now suppose Sean makes n = 30 rolls, and a 6 comes up 6 times out of the 30 rolls. Determine the P-value of the test, giving your answer to 4 decimal places. Please use 3 decimal places in your test statistic when finding the P-value. P-value = ⠀⠀ (c) Answer the question: Does this sample provide evidence at the 5 percent level that Sean rolls a 6 more often than you'd expect? (Type: Yes or No) 4

Matt thinks that he has a special relationship with the number 2. In particular, Matt thinks that he would roll a 2 with a fair 6-sided die more often than you'd expect by chance alone. Suppose p is the true proportion of the time Matt will roll a 2. (a) State the null and alternative hypotheses for testing Matt's claim. (Type the symbol "p" for the population proportion, whichever symbols you need of "", "=", "not =" and express any values as a fraction e.g. p = 1/3) Ho p= 1/6 = Ha= p > 1/6 (b) Now suppose Matt makes n = 34 rolls, and a 2 comes up 7 times out of the 34 rolls. Determine the P-value of the test: P-value = | (c) Answer the question: Does this sample provide evidence at the 5 percent level that Matt rolls a 2 more often than you'd expect? (Type: Yes or No) no

A farmer only grows apple and orange trees in his orchard. 40% of his trees are apple trees. He is concerned that a parasite may be infecting his trees. The probability of the parasite infecting a given apple tree is 5% and the probability of the parasite infecting a given orange tree is 3%. Please give your answers to 3 decimal places, for example 0.305. a) What proportion of his trees are infected by the parasite? Your answer is 1 b) If a given tree is not infected, what is the probability that this tree was an apple tree? Your answer is

A humane society claims that less than 62% of households in a certain country own a pet. In a random sample of 500 households in that country, 290 say they own a pet. At a = 0.05, is there enough evidence to support the society's claim? Complete parts (a) through (c) below. (a) Identify the claim and state Ho and H Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) O A. Less than % of households in the country own a pet. O B. % of households in the country own a pet. O C. The percentage households in the country that own a pet is not %. O D. More than % of households in the country own a pet. Let p be the population proportion of successes, where a success is a household in the country that owns a pet. State Ho and H.. Select the correct choice below and fill in the answer boxes to complete your choice. (Round to two decimal places as needed.) CO A. Hnipz O B. Hnip= OC.…

Find the probability ​P(Ec​) if ​P(E)=0.17.

A certain disease has an incidence rate of 0.2%. The false negative rate is 8%, and the false positive rate is 3%. Calculate the probability that a person who tests positive actually has the disease. 0.0848 Note: The incidence rate is the probability that a random person gets the disease. The false negative rate is the probability of getting a negative result given that the person has the disease. The false positive rate is the probability of getting a positive result given that the person does not have the disease.

Solve a,b