7.10 Topic 10: Inference for One Proportion 78. Choose the correct word (s) to fill in the blank for each sentence. (a) A point estimate is obtained from the (sample/population) (b) A point estimate is used to make inferences about the (sample statistic/population parameter) (C) As the sample size decreases, the width of the confidence interval (increases/decreases/does not change) (a) As the level of confidence increases, the width of the confidence interval (increases/decreases/does not change) (e) As the point estimate increases, the width of the confidence interval (increases/decreases/does not change) (sample/population) (f) Interpretations of a cofidence interval are always in terms of the 79. What is the multiplier for an interval that estimates the proportion with (a) 88% confidence? (b) 98% confidence? 80. Research commissioned by AT&T and conducted by Braun Research in 2015 polled 2,00 in the U.S. aged 16-65 who use their smartphone and drive at least once a day. An unsettling 17% of the respondents admitted to taking pictures/selfies while driving. (a) What is the point estimate for the proportion of drivers who take pictures with a smartphone while driving? (b) What is the multiplier for a 90% confidence interval to estimate the proportion of drivers who take photos? (c) What is the standard error for the proportion who take photos? (d) What is the margin of error? (e) Construct a confidence interval for proportion of all drivers who take pictures while driving. (f) Interpret the interval. (g) A friend claims that 25% of drivers take pictures while behind the wheel? Is your friend's claim valid? Explain. 81. Research commissioned by AT&T and conducted by Braun Research in 2015 polled 2,067 people in the U.S. aged 16-65 who use their smartphone and drive at least once a day. When asked if they used Facebook while driving, 558 respondents answered "yes". (a) What is the point estimate for the proportion of drivers who access Facebook while driving? (b) What is the margin of error for a 95% confidence interval? (c) Construct a confidence interval for proportion of all drivers who take pictures while driving. (d) Interpret the interval. (e) An independent researcher claims that 30% of drivers use Facebook behind the wheel. Based on the interval, is the claim valid? Explain.

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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.