Question 3: A travel agent wants to know if the proportions of satisfied customers at two different resorts are different. In a random sample of 200 customers at Resort A, 160 were satisfied. In a random sample of 250 customer at Resort B, 172 were satisfied. At the 1% level of significance, do the resorts differ in customer satisfaction? (a) State the hypotheses for this test and define one of the parameters of interest in full context. (b) Verify that the assumptions for the test are met. 1. Independent Groups Assumption: 2. Independence Assumption, checked by the Randomization Condition: 3. Sample Size Assumption, checked by the Success/Failure Condition: (c) Under the null hypothesis, compute the ingredients needed to calculate the test statistic. Pi – P2 = E(fi – P2) = Ppool = SEpool (P1 – P2) = (d) Compute the test statistic for this test. (e) Draw a rough normal diagram for this test statistic and compute the p-value for the test. 62.171 Introductory Statistics Lab Assignment 8 Page 3 of 3 (f) Assess the significance of this test: (g) Make a conclusion for this test in full context. (h) To estimate how different the two population proportions are, we will compute a 99% con- fidence interval. What are the unpooled standard error and critical value? SE(îi – P2) = (i) Compute the 99% confidence interval.
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.
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