Solving Analysts' Inflation Prediction Problems

In summary, we have a conversation discussing various problems that require probability calculations. The first problem involves a random sample of 15 analysts predicting inflation rates, where the probability is 0.01 that the sample standard deviation is larger than a certain number and 0.025 that it is smaller than another number. The next question asks for a pair of numbers such that the probability of the sample standard deviation lying between them is 0.90. The next problem involves a medicine company concerned about the mean weight and variance of an active ingredient in their pills. A random sample of 20 pills is selected and found to have a sample variance of 2.05, and the question asks for the likelihood of finding a sample variance this high or
  • #1
mouse
19
0
the following problems i have trouble solving, please help: :smile:

each member of a random sample of 15 analysts was asked to predict the rate of inflation for the coming year. assume that the predictions for the whole population of analysts follow a normal distribution with the standard deviation 1.8%.

a) the probability is .01 that the sample standard deviation is bigger than what number?

b) the probability is .025 that the sample standard deviation is smaller than what number?

c) find any pair of numbers such that the probbility that the sample standard deviation lies between these numbers is .90.


a medicine company produces pills containing an active ingredient. the company is concerned about the mean weight of this ingredient per pill, but it also requires that the variance be no more than 1.5. a random sample of 20 pills is selected, and the sample variance is found to be 2.05. how likely is it that a sample variance this high or higher would be found if the population variance is in fact 1.5? assume that the population distribution is normal.
:confused:

thanks.
 
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  • #2
i can use another help with this problem, driving me nuts all day long:

montly rates of return on the share of a stock are independent of one another and normally distributed with a standard deviation of 1.7. a sample of 12 months is taken.

a) find the probability that the sample standard deviation is less than 2.5.

b) find the probability that the sample standard deviation is bigger than 1.0.

thanks
 
  • #3


I would approach these problems by using statistical analysis and probability theory. For the first problem, we are given a sample of 15 analysts with their predictions for the rate of inflation. We are also told that the population of analysts' predictions follows a normal distribution with a standard deviation of 1.8%.

a) To find the probability that the sample standard deviation is bigger than a certain number, we can use the chi-square distribution. The formula for this is:

P(S > x) = 1 - χ^2(df, α/2)

Where S is the sample standard deviation, x is the desired number, df is the degrees of freedom (n-1 in this case), and α is the significance level (0.01 in this problem).

Plugging in the numbers, we get:

P(S > x) = 1 - χ^2(14, 0.005)

Using a chi-square calculator, we get x = 3.433. Therefore, there is a 0.01 probability that the sample standard deviation is bigger than 3.433.

b) Similarly, to find the probability that the sample standard deviation is smaller than a certain number, we can use the same formula as above, but with a different significance level.

P(S < x) = χ^2(df, α/2)

Plugging in the numbers, we get:

P(S < x) = χ^2(14, 0.0125)

Using a chi-square calculator, we get x = 0.272. Therefore, there is a 0.025 probability that the sample standard deviation is smaller than 0.272.

c) To find a pair of numbers such that the probability that the sample standard deviation lies between them is 0.90, we can use the same formula as above, but with different significance levels.

P(x1 < S < x2) = χ^2(df, α/2) - χ^2(df, 1-α/2)

Plugging in the numbers, we get:

P(x1 < S < x2) = χ^2(14, 0.05) - χ^2(14, 0.95)

Using a chi-square calculator, we get x1 = 0.028 and x2 =
 

1. What is the purpose of solving analysts' inflation prediction problems?

The purpose of solving analysts' inflation prediction problems is to accurately forecast future levels of inflation, which is a measure of the overall increase in prices of goods and services over time. This information is crucial for businesses, investors, and policy makers to make informed decisions and prepare for potential economic changes.

2. How do analysts usually predict inflation?

Analysts typically use statistical models and economic indicators to forecast inflation. These models take into account factors such as consumer spending, unemployment rates, and monetary policy to estimate future levels of inflation.

3. What are the biggest challenges in solving inflation prediction problems?

One of the biggest challenges in solving inflation prediction problems is the volatility and unpredictability of economic conditions. Inflation can be influenced by a wide range of factors, making it difficult to accurately forecast. Additionally, the accuracy of predictions can be affected by changes in the economy or unexpected events, such as natural disasters or political changes.

4. How important is it for analysts to accurately predict inflation?

Accurate inflation predictions are crucial for businesses, investors, and policy makers to make informed decisions. Inflation can have a significant impact on consumer purchasing power, interest rates, and overall economic stability. Therefore, it is important for analysts to strive for accuracy in their predictions.

5. What are some strategies for improving inflation prediction accuracy?

There are several strategies that analysts can use to improve inflation prediction accuracy. These include using a combination of different models, regularly updating and adjusting the models to reflect changing economic conditions, and incorporating qualitative analysis and expert opinions in addition to quantitative data. Additionally, continuously monitoring and analyzing economic indicators can help improve the accuracy of predictions.

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