A movie production company is releasing a movie with the hopes of many viewers returning to see the movie in the theater for a second time. Their target is to have 30 million viewers, and they want more than 30% of the viewers to return to see the movie again. They show the movie to a test audience of 200 people, and after the movie they asked them if they would see the movie in theaters again. Of the test audience, 68 people said they would see the movie again. (You may find it useful to reference the appropriate table: z table or t table) a. Specify the competing hypotheses to test if more than 30% of the viewers will return to see the movie again. multiple choice 1 H0: p = 0.30; HA: p ≠ 0.30 H0: p ≥ 0.30; HA: p < 0.30 H0: p ≤ 0.30; HA: p > 0.30 b-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) b-2. Find the p-value. multiple choice 2 p-value < 0.01 0.01 ≤ p-value < 0.025 0.025 ≤ p-value < 0.05 0.05 ≤ p-value < 0.10 p-value ≥ 0.10 c. At the 5% significance level, what is the conclusion? multiple choice 3 Reject H0, the population proportion is greater than 0.30. Reject H0, the population proportion is not greater than 0.30. Do not reject H0, the population proportion is greater than 0.30. Do not reject H0, the population proportion is not greater than 0.30.
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.
A movie production company is releasing a movie with the hopes of many viewers returning to see the movie in the theater for a second time. Their target is to have 30 million viewers, and they want more than 30% of the viewers to return to see the movie again. They show the movie to a test audience of 200 people, and after the movie they asked them if they would see the movie in theaters again. Of the test audience, 68 people said they would see the movie again. (You may find it useful to reference the appropriate table: z table or t table)
a. Specify the competing hypotheses to test if more than 30% of the viewers will return to see the movie again.
multiple choice 1
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H0: p = 0.30; HA: p ≠ 0.30
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H0: p ≥ 0.30; HA: p < 0.30
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H0: p ≤ 0.30; HA: p > 0.30
b-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)
b-2. Find the p-value.
multiple choice 2
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p-value < 0.01
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0.01 ≤ p-value < 0.025
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0.025 ≤ p-value < 0.05
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0.05 ≤ p-value < 0.10
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p-value ≥ 0.10
c. At the 5% significance level, what is the conclusion?
multiple choice 3
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Reject H0, the population proportion is greater than 0.30.
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Reject H0, the population proportion is not greater than 0.30.
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Do not reject H0, the population proportion is greater than 0.30.
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Do not reject H0, the population proportion is not greater than 0.30.
d. Repeat the analysis at a 10% level of significance.
multiple choice 4
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Reject H0
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Do not reject H0
e. Interpret your results.
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