Suppose you work for a news agency, which is conducting an exit poll for the MCD (Municipal Corporation of Delhi) elections. You have been tasked with predicting the winner for ward 75N (Ashok Vihar). You ask 100 randomly selected voters from this ward to name the party they had voted for. Of the 100 voters, 58 voted for AAP and 42 voted for BJP. So, you define X as the proportion of people that voted for AAP. Then, the frequency distribution for X would be as shown in the table given below. X Frequency1 580 42Question 2/3MandatoryComprehensionLet’s say you wish to construct a sampling distribution of sample size 100 for the proportion of people that voted for AAP. Suppose the population standard deviation is known to be 0.7, what is the interval in which the mean of the sampling distribution will belong at a 90% confidence level?(0.485, 0.675) (0.572, 0.588)(0.465, 0.695)(0.503, 0.657)
Question
Suppose you work for a news agency, which is conducting an exit poll for the MCD (Municipal Corporation of Delhi) elections. You have been tasked with predicting the winner for ward 75N (Ashok Vihar). You ask 100 randomly selected voters from this ward to name the party they had voted for. Of the 100 voters, 58 voted for AAP and 42 voted for BJP. So, you define X as the proportion of people that voted for AAP. Then, the frequency distribution for X would be as shown in the table given below. X Frequency1 580 42Question 2/3MandatoryComprehensionLet’s say you wish to construct a sampling distribution of sample size 100 for the proportion of people that voted for AAP. Suppose the population standard deviation is known to be 0.7, what is the interval in which the mean of the sampling distribution will belong at a 90% confidence level?(0.485, 0.675) (0.572, 0.588)(0.465, 0.695)(0.503, 0.657)
Solution
To answer this question, we need to use the formula for the confidence interval for a population mean. The formula is:
Confidence Interval = X̄ ± Z * (σ/√n)
Where:
- X̄ is the sample mean
- Z is the Z-score (which corresponds to the desired confidence level)
- σ is the population standard deviation
- n is the sample size
In this case:
- X̄ = 0.58 (the proportion of people that voted for AAP)
- Z = 1.645 (Z-score for a 90% confidence level)
- σ = 0.7 (given in the question)
- n = 100 (the sample size)
Substituting these values into the formula, we get:
Confidence Interval = 0.58 ± 1.645 * (0.7/√100) = 0.58 ± 1.645 * 0.07 = 0.58 ± 0.11515
So, the interval in which the mean of the sampling distribution will belong at a 90% confidence level is (0.58 - 0.11515, 0.58 + 0.11515) = (0.46485, 0.69515).
Therefore, the closest option to this result is (0.465, 0.695).
Similar Questions
You ask 100 randomly selected voters from this ward to name the party they had voted for. Of the 100 voters, 58 voted for AAP and 42 voted for BJP. So, you define X as the proportion of people that voted for AAP. Then, the frequency distribution for X would be as shown in the table given below. X Frequency1 580 42Question 1/3MandatoryComprehensionFind the mean and standard deviation of X.
A frequency distribution shows the number of data values falling within each class.Group of answer choicesTrueFalse
Suppose Facebook has launched a new fact-checking feature. It conducts a survey among its user base, wherein it asks them the question ‘Do you find the fact-checking feature useful?’. Out of the 2,500 respondents, 53.2% believe that the feature is useful. If you define X as the proportion of people that find the feature useful, the frequency distribution for X would be as shown in the table given below. X Frequency1 1,3300 1,170Question 1/3MandatorySampling and EstimationFind the mean and standard deviation of X.0.532; 0.3460.532; 0.2490.532; 0.499None of the above
Which of the following represents the proportion of the total number of observations that fall at or below the upper limit of each group?Group of answer choicesPercentilePareto chartFrequency DistributionCumulative Relative Frequency
A relative frequency distribution describes the proportion of data values that fall within each category.Group of answer choicesTrueFalse
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.