Question

QUESTION l. An investigation has been carried out in a region to know the perception of "citizen insecurity" of its inhabitants. 1,270 people in the region were interviewed, of which 27.1% responded that it was a "serious" problem. Knowing that this opinion was previously held by 25.3% of the population of that region, we want to know if said opinion has changed significantly for a confidence level of 97.2%. Taking this statement into account, the following is requested: a) Critical value of the contrast statistic. b) Solve the hypothesis test and indicate what conclusion we can reach. c) P-value of contrast.

265

likes
1324 views

Answer to a math question QUESTION l. An investigation has been carried out in a region to know the perception of "citizen insecurity" of its inhabitants. 1,270 people in the region were interviewed, of which 27.1% responded that it was a "serious" problem. Knowing that this opinion was previously held by 25.3% of the population of that region, we want to know if said opinion has changed significantly for a confidence level of 97.2%. Taking this statement into account, the following is requested: a) Critical value of the contrast statistic. b) Solve the hypothesis test and indicate what conclusion we can reach. c) P-value of contrast.

Expert avatar
Bud
4.6
96 Answers
To test whether the opinion about "citizen insecurity" has changed significantly in the region, you can perform a hypothesis test. Let's set up the hypothesis test and calculate the critical value, conduct the test, and find the p-value. **Hypotheses:** - Null Hypothesis (H0): The proportion of people who consider "citizen insecurity" a "serious" problem remains the same as before, i.e., p = 0.253 (no change). - Alternative Hypothesis (Ha): The proportion of people who consider "citizen insecurity" a "serious" problem has changed significantly, i.e., p ≠ 0.253. **Given Data:** - Sample size (n) = 1,270 - Proportion from the sample (p̂) = 27.1% or 0.271 - Proportion before (p) = 25.3% or 0.253 - Confidence level = 97.2% **a) Critical Value of the Contrast Statistic:** To find the critical value for the two-tailed test at a 97.2% confidence level, we'll use a Z-table or a calculator. The critical values for a two-tailed test at this confidence level are approximately ±2.64 (you can find this value from a standard normal distribution table or calculator). **b) Hypothesis Test:** We'll perform a two-tailed Z-test using the given data: 1. Calculate the standard error: Standard Error (SE) = sqrt[(p(1-p))/n] SE = sqrt[(0.253 * 0.747) / 1270] SE ≈ 0.0127 2. Calculate the Z-test statistic: Z = (p̂ - p) / SE Z = (0.271 - 0.253) / 0.0127 Z ≈ 1.417 3. Compare the Z-test statistic to the critical value: Since it's a two-tailed test, we compare the absolute value of Z to the critical value. |1.417| < 2.64 **Conclusion:** The absolute Z-test statistic (|Z|) is less than the critical value (2.64). Therefore, we fail to reject the null hypothesis (H0). This means that there is no significant evidence to conclude that the proportion of people who consider "citizen insecurity" a "serious" problem has changed significantly in the region. **c) P-Value of the Contrast:** To find the p-value, you can use a standard normal distribution table or calculator. The p-value is the probability of observing a test statistic as extreme as the one calculated (Z ≈ 1.417) under the null hypothesis. For Z ≈ 1.417, the two-tailed p-value is approximately 0.156 (from a standard normal distribution table). Since this p-value is greater than the typical significance level (alpha), which is usually set at 0.05, it also supports the conclusion of failing to reject the null hypothesis. There is no strong evidence of a significant change in the perception of "citizen insecurity" in the region.

Frequently asked questions (FAQs)
What are the characteristics of an ellipse function with a major axis of length 10 and a minor axis of length 6?
+
Question: What is the measure of the third angle in an isosceles triangle if one angle measures 80°?
+
What is the mean, mode, median, range, and average of the following data set: 2, 5, 5, 7, 8, 9, 12, 15?
+
New questions in Mathematics
Find an arc length parameterization of the curve that has the same orientation as the given curve and for which the reference point corresponds to t=0. Use an arc length s as a parameter. r(t) = 3(e^t) cos (t)i + 3(e^t)sin(t)j; 0<=t<=(3.14/2)
One contestant on a game show has 1,500 points and another contestant has -250 points. What is the difference between the scores of the contestants?
The profit G of the company CHUNCHES SA is given by G(x) = 3×(40 – ×), where × is the quantity of items sold. Find the maximum profit.
x/20*100
The mean temperature for july in H-town 73 degrees fahrenheit. Assuming that the distribution of temperature is normal what would the standart deviation have to be if 5% of the days in july have a temperature of at least 87 degrees?
A regional candy factory sells a guava roll at a price of $48, the monthly fixed costs amount to $125,000 and the variable cost for making a guava roll is $28. Determine: a) The equation of the total income from the production of guava rolls.
Solve this mathematical problem if 3/5 of a roll of tape measures 2m. How long is the complete roll?
A construction company is working on two projects: house construction and building construction. Each house requires 4 weeks of work and produces a profit of $50,000. Each building requires 8 weeks of work and produces a profit of $100,000. The company has a total of 24 work weeks available. Furthermore, it is known that at least 2 houses and at least 1 building must be built to meet the demand. The company wants to maximize its profits and needs to determine how many houses and buildings it should build to meet demand and maximize profits, given time and demand constraints.
15/5+7-5
The thermal representation f(x) = 20 times 0.8 to the power of x is known from an exponential function f. Specify the intersection point with the y-axis
Buffalo Company makes and sells shampoo. Each unit requires $1.40 labor costs, material costs per unit are $0.90 and other variable costs are $0.30. It sells shampoo for $4.45 to retailers. Fixed costs are $15,000. It sold 25,000 units in the current month. What is the Break-Even point in units? What is the Break-Even point in dollars? What is the contribution margin of Buffalo Company?
The mass of 120 molecules of X2C4 is 9127.2 amu. Identify the unknown atom, X, by finding the atomic mass. The atomic mass of C is 12.01 amu/atom
Find the vertex F(x)=x^2-10x
A property sold for $745,000 in a co-brokered transaction. The seller has agreed to pay a 7% commission to the listing firm. The listing firm has agreed to equally split the commission with the selling firm. If the buyer’s broker will receive 8% of the selling firm’s commission, how much commission will the buyer’s broker receive? $14,900 $3725 $$37250 $18625
Find the set of points formed by the expression 𝜋<|𝑧−4+2𝑖|<3𝜋.
Find I (Intrest) using simple interest formula of 17700 @ 15% for 4 years
A candy manufacturer must monitor deviations in the amount of sugar in their products They want their products to meet standards. They selected a random sample of 20 candies and found that the sandard deviation of that sample is 1.7. What is the probabilty of finding a sample variance as high or higher if the population variance is actually 3277 Assume the population distribution is normal.
-1/3x+15=18
Sarah is lining a square tray with 1 inch square tiles. the side length of the tray is 9 inches. How many tiles does Sarah need?
A person travels by car from one city to another with different constant speeds between pairs of cities. She drives for 55.0 min at 100.0 km/h, 14.0 min at 65.0 km/h, and 45.0 min at 60.0 km/h and spends 20.0 min eating lunch and buying gas. (a) Determine the average speed for the trip.