14. There appears to be some evidence suggesting that earlier retirement may lead to memory decline (Rohwedder & Willis, 2010). The researchers gave a memory test to men and women aged 60–64 in several countries that have different retirement ages. For each country, the researchers recorded the average memory score and the percentage of individuals in the 60–64 age range who were retired. Note that a higher percentage retired indicates a younger retirement age for that country. The following data are similar to the results from the study. Country % Retired (X) Memory Score (Y) Sweden 39 9.3 U.S.A. 48 10.9 England 59 10.7 Germany 70 9.1 Spain 74 6.4 Netherlands 78 9.1 Italy 81 7.2 France 87 7.9 Belgium 88 8.5 Austria 91 9.0 (1) Identify the two hypotheses. (2) Determine the critical region for your decision (use α = 0.05). (3) Compute the test statistic. (4) Use the test statistic to make a decision and interpret that decision.
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.
14. There appears to be some evidence suggesting that earlier retirement may lead to memory decline
(Rohwedder & Willis, 2010). The researchers gave a memory test to men and women aged 60–64 in
several countries that have different retirement ages. For each country, the researchers recorded the average memory score and the percentage of individuals in the 60–64 age
Country % Retired (X) Memory Score (Y)
Sweden 39 9.3
U.S.A. 48 10.9
England 59 10.7
Germany 70 9.1
Spain 74 6.4
Netherlands 78 9.1
Italy 81 7.2
France 87 7.9
Belgium 88 8.5
Austria 91 9.0
(1) Identify the two hypotheses.
(2) Determine the critical region for your decision (use α = 0.05).
(3) Compute the test statistic.
(4) Use the test statistic to make a decision and interpret that decision.
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