82. The Vegetarian Resource Group commissioned Harris Poll in 2016 to conduct a nationally repre- sentative online poll of 2,015 adults aged 18 and over. They found that 3.3% of the respondents (a) Construct and interpret a 95% confidence interval for the proportion of vegetarians. (b) Explain why a 90% confidence interval for the proportion of vegetarians will be wider/narrower (c) Explain why the interval will be wider/narrower than the one in (a) if the sample size identified as vegetarian. than the one in (a). Construct the interval to confirm. changed to n = 300. Construct the interval to confirm. 83. Choose the correct word(s) to fill in the blank for each sentence. (a) The hypotheses are always stated in terms of (b) Any numbers in the hypotheses come from the (olan (c) The test statistic and p-value assume the (statistics/parameters) (data/research question) (null/alternative/data) is true (null/alternative) hypothesis (d) The conclusion is always in terms of the 84. Choose the correct word(s) to fill in the blank for each sentence. akgosq (a) If the null is true in reality, we would expect the test statistic tO De (small/large) (b) If the alternative is true in reality, we would expect the test statistic to be (small/large) nothing else changed besides an increase in sample size, the test statistic would be (smaller/larger) (d) If nothing else changed besides an increase in sample size, the p-value in a two sided test would be (smaller/larger) 05. According to NAFSA, 1.55% of all college students in the US studied abroad during the 2014-2015 academic year. Being the location of our country's capitol, a researcher believes that a nigiei proportion of students study abroad in the District of Columbia than elsewhere in the country. Suppose a random sample of 250 college students from D.C. had 15 who studied abroad. (a) State the hypotheses in symbols and words to test the researcher's claim. (b) Calculate the test statistic. (c) Calculate the p-value. (d) Interpret the p-value. (e) State the conclusion of the test. 86. Movie theaters make as much as 85% profit on items sold at the concession stand. Without snacks at the movies, there would be no movies! A theater owner suspected that less than half of his customers purchased food at the concession counter. To examine this claim, a random sample of 80 patrons was selected and 35 of them purchased food. (a) State the hypotheses in symbols and words to test the theater owner's claim. (b) Calculate the test statistic. (c) Calculate the p-value. (d) Interpret the p-value. (e) State the conclusion of the test.
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Question 86 parts D and E
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