Unemployment rate

Over the last 16 years, the country's unemployment rate has changed according to the following frequency table:
years of unemployment: 2 5 2 3 3 1
unemploymen rate: 0.5 1 1.5 2 2.5 3 in % (percent).

Determine the two-sided confidence interval for the variance DN with a confidence level of 0.95.

Correct answer:

a =  1.224 %
b =  1.9635 %

Step-by-step explanation:

n=2+5+2+3+3+1=16 α=0.95  μ=2 0.5+5 1+2 1.5+3 2+3 2.5+1 3n=2 0.5+5 1+2 1.5+3 2+3 2.5+1 316=51321.5938  E2=2 (0.5μ)2+5 (1μ)2+2 (1.5μ)2+3 (2μ)2+3 (2.5μ)2+1 (3μ)2=2 (0.51.5938)2+5 (11.5938)2+2 (1.51.5938)2+3 (21.5938)2+3 (2.51.5938)2+1 (31.5938)2=583649.1094  V=E2/n=9.1094/16=58310240.5693  σ=V=0.56930.7545 α=0.95 α2=1(10.95)/2=3940=0.975 u(0.975)=1.96 u=1.96  r=u σ/n=1.96 0.7545/160.3697  a=μr=1.59380.3697=1.224%
b=μ+r=1.5938+0.3697=1.9635%



Did you find an error or inaccuracy? Feel free to write us. Thank you!






avatar




Tips to related online calculators
Looking for help with calculating arithmetic mean?
Looking for a statistical calculator?
Looking for a standard deviation calculator?
Our percentage calculator will help you quickly calculate various typical tasks with percentages.

You need to know the following knowledge to solve this word math problem:


 
We encourage you to watch this tutorial video on this math problem: video1   video2

Related math problems and questions:

  • Three sigma rule
    stromy The height of trees in a given stand is known to be a quantity with a normal probability distribution with a mean value of 15 m and a variance of 5 m2. Determine the interval in which there will be tree heights in such a stand with a probability of 90%
  • Standard deviation
    standard-dev Find standard deviation for dataset (grouped data): Age (years) No. Of Persons 0-10 15 10-20 15 20-30 23 30-40 22 40-50 25 50-60 10 60-70 5 70-80 10
  • Confidence Interval
    normal_d The average grade of 50 students senior students in a statistics class is 85 with a standard deviation of 10.2 while a group of 60 senior students got an average of 80 with a standard deviation of 8.9, can the difference in the mean grade be attributed to
  • Confidence interval
    normal_d A food testing laboratory in Abu Dhabi has been commissioned to carry out an estimate of the amount of olive oil contained in 1-gallon tins purchased from a range of international olive oil producers. The manufacturers state that the standard deviation of
  • Complaints
    statistics The table is given: days complaints 0-4 2 5-9 4 10-14 8 15-19 6 20-24 4 25-29 3 30-34 3 1.1 What percentage of complaints were resolved within 2weeks? 1.2 calculate the mean number of days to resolve these complaints. 1.3 calculate the modal number of day
  • Chi square
    chi_squared A manufacturer of phone batteries claims that his batteries' lives are approximately normally distributed with a standard deviation equal to 0.9 years. If a random sample of 10 of these batteries has a standard deviation of 1.2 years. Do you think that th
  • SD - mean
    normal_sd The mean is 10 and the standard deviation is 3.5. If the data set contains 40 data values, approximately how many of the data values will fall within the range of 6.5 to 13.5?
  • A professor
    skola A professor in a typing class found out that the average performance of an expert typist is 85 words per minute. A random sample of 16 students took the typing test and an average speed of 62 words per minute was obtained with a standard deviation of 8. C
  • Normal Distribution
    normal_d At one college, GPA's are normally distributed with a mean of 3.1 and a standard deviation of 0.4. What percentage of students at the college have a GPA between 2.7 and 3.5?
  • Inflation
    tsar Once upon a time, tsar owned a money printer and printed and printed. The result of printing money prices went up,in the first year 3.9 %, in the second 6%, in the third 4.7% and in the fourth 5.5%. Then tsar was failed in election. Calculate the average
  • Performance comparing
    statistics A standardized test was administered to thousands of students with a mean score of 85 and a standard deviation of 8. A random sample of 50 students were given the same test and showed an average score of 83.20. Is there evidence to show that this group ha
  • Energy
    energy In one region, the September energy consumption levels for single-family homes are found to be normally distributed with a mean of 1050 kWh and a standard deviation of of 218 kWh. Find the consumption level separating the bottom 45% from the top 55%.
  • IQ Intelligence quotient
    normal_d Intelligence quotient (IQ) is a standardized score used as the output of standardized intelligence psychological tests to quantify a person's intelligence with the rest of the population (respectively to a given group). Intelligence has an approximately n
  • Tallest people a
    normal_d As a group, the Dutch are amongst the tallest people in the world. The average Dutchman is 184 cm tall. If a normal distribution is appropriate, and the standard deviation for Dutchmen is about 8 cm, what is the percentage of Dutchmen who will be over 2 m
  • Ball bearings
    normal_d One bearing is selected from the shipment of ball bearings. It is known from previous deliveries that the inner bearing radius can be considered as a normal distribution of N (µ = 0.400, σ2 = 25.10^−6). Calculate the probability that the selected radius w
  • Doctors
    doktori The drug successfully treats 90% of cases. Calculate the probability that he will cure at least 18 patients out of 20?
  • Controller
    std_dev Output Controller of the company in the control of 50 randomly selected products found that 37 of them had no defects, 8 has only one flaw, three had two defects, and two products had three defects. Determine the standard deviation and coefficient of vari