During the days of coronavirus, people work most of the time from home. Many offices, schools, universities conduct their works, meetings, classes online. As a result of this new normal, it is assumed that on average, utility expenses per family (electricity, water, gas etc.) increases by 40% per month. For the verification of this assumption, four months data of percentage change of utility expenses of 10 families of similar size is given below and answer the following questions, the data is normally distributed: Percentage change of utility expenses April 33.65 37.09 29.72 33.42 38.14 34.9 37.35 38.66 22.92 34.19 May 37.19 36.61 40.35 28.19 35.19 37.43 38.03 42.99 30.22 3
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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During the days of coronavirus, people work most of the time from home. Many offices, schools, universities conduct their works, meetings, classes online. As a result of this new normal, it is assumed that on average, utility expenses per family (electricity, water, gas etc.) increases by 40% per month. For the verification of this assumption, four months data of percentage change of utility expenses of 10 families of similar size is given below and answer the following questions, the data is
|
|
Percentage change of utility expenses |
|||||||||
|
April |
33.65 |
37.09 |
29.72 |
33.42 |
38.14 |
34.9 |
37.35 |
38.66 |
22.92 |
34.19 |
|
May |
37.19 |
36.61 |
40.35 |
28.19 |
35.19 |
37.43 |
38.03 |
42.99 |
30.22 |
38.8 |
|
June |
37.13 |
36.2 |
43.6 |
35.31 |
33.66 |
28.51 |
37.67 |
20.68 |
38.04 |
38.43 |
|
July |
38.84 |
32.17 |
34.9 |
30.17 |
29.63 |
27.14 |
32.17 |
33.46 |
36.72 |
39.64 |
- Which statistical technique(s) will be suitable for testing this assumption? (Only write the name(s) of all possible techniques)
- Write tabulated value of test statistic at 0.05 level of significance
- Write the null and alternative hypothesis for this test.
- Write your final conclusion about the assumption.
- What will be the 95% confidence interval for the average percentage change of utility expenses on the basis of given data.
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