STAT_HW-2

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STAT-515 HOMEWORK-02 ADITYA PARAVASTU G01457323

QUESTION-2 1)Explain what the ‘Point Estimator’ and the ‘Interval Estimator’ is. A) Point estimator: Assigns a number that is a "best guess" for a desired parameter (such as the population mean). Consider the sample mean (x). Interval Estimator : Provides possible parameter values (interval). Example: 95% confidence interval of the population. 2) Do y ou prefer the ‘Point Estimator’ or the ’ Interval Estimator’. Explain by giving examples. A) I usually choose interval estimators. An interval estimator, in contrast to a point estimator, provides the range in which the parameter is expected to remain, which is often very helpful in real world situations for example, in clinical trials, an interval estimator will provide the range of in which a specific impact of drug falls, more context on change and includes detailed information. 3) What is ‘Confidence Interval’ and what does 95% confidence interval mean? A) Confidence Interval (CI): This interval estimate provides a range of coefficients derived from the data sample and most likely the value of an unknown population parameter. 95% confidence interval: This means that we predict that if we construct a CI for any of the number of samples, about 95% of the intervals will contain the true parameter value. 4) What is ‘Hypothesis Testing’? A) Hypothesis testing is used to make statistical inferences or conclusions about a population from a sample of data. This involves formulating initial hypotheses (invalid hypotheses), collecting data, and then deciding whether to accept or reject those initial hypotheses based on the likelihood of having the observed data as an opinion if the first is true.

5) How does Hypothesis testing used in Data science. Explain by using real- life examples? A) In data science, hypothesis testing can be used to determine whether a variable (such as a new part of the website) has a significant impact. For example, an eCommerce platform might conduct A/B testing to increase customer engagement where Group A uses the new feature and Group B does not. Perhaps useful in hypothesis testing to determine whether any observed increase in Group A exposure is statistically significant. 6) What are the errors in Hypothesis testing ? A) 1. Type 1 Error (False Positive): This error occurs when we incorrectly reject the true null hypothesis. Specifically, we find evidence that there is no real difference or effect in the population. Probability of Type I error = α (Alpha), which is the level of validity of the test. Type 2 error (False NegativeNot rejecting the null hypothesis when it's false (False Negative). Type 2 Probability of error = (beta). 7) Suppose that, in a hypothesis test, the null hypothesis is in fact true. Is it possible to make a ‘Type 2’ error. Explain . A) No, we only get a Type 2 error if we fail to reject the null hypothesis as false. If the null hypothesis is correct and we don ’t reject it, then that’s a wise choice and not a mistake. 8) Explain the difference between the ‘significance level’ and the ‘confidence level’ and identify the relationship between them. A) Significance level: The false probability when the null hypothesis is true (causing a type-1 error) is known as the significance level, which is sometimes indicated by a symbol The null hypothesis will be rejected if it falls below this point, which it is supposed to do.

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Confidence level : The number of possible confidence intervals containing the actual value of the unknown parameter is represented by the confidence level, stated as a percentage. 9) What is a ‘rejection region’ in Hypothesis testing and what is the ‘P - value’? A) The range of values over which we reject the null hypothesis is known as the rejection region. depending on its relevance. In the event that the null hypothesis is correct, the probability of finding the test statistic is at least as strong as the actual finding, known as the "P-value". 10) If it is important not to reject the true null hypothesis, should the hypothesis test performed at a smaller significance level? If the P-value for the hypothesis test is 0.044. Decide the significance level that you select and the decision. A) If it is important to avoid rejecting the correct null hypothesis, a lower significance threshold (such as = 0.01) should be considered to reduce Type 1 error. A P-value of 0.044 indicates: We reject the null hypothesis because P is positive if = 0.05. Since P >, we do not rule out the null hypothesis if = 0.01. Decisions must be in line with the situation and possible negative effects of Type 1 and Type 2 faults in particular applications.

QUESTION-1: library(leaflet) library(tidyverse) datafr=read.csv("C:\\Users\\DELL\\Downloads\\Japan_earthquakes(1).csv") n=leaflet(datafr) %>% addTiles() %>% addMarkers(~longitude, ~latitude, popup = ~place) n The dataset is loaded as a CSV file named "Japan_earthquakes(1).csv" and addTiles are used to add tiles. datafr_sub= subset(datafr,datafr$mag> 6.00) sub_n= leaflet(datafr_sub) %>% addTiles() %>%

addMarkers( ~longitude, ~latitude, popup = ~place) sub_n A new data is stored in datafr_sub library(dplyr) datafr= datafr %>% mutate(radius = 10^(-mag/2)) z=leaflet(datafr) %>% addTiles() %>% addCircles(~longitude, opacity = 2, color = 'green',

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~latitude, radius = ~radius, label = ~place) %>% addPopups( lat = ~latitude, lng = ~longitude, popup = ~paste( "Time: ", datafr_sub$time, "<br>", "Magnitude: ", datafr_sub$mag, "<br>", "Depth (km): ", datafr_sub$depth, "<br>", "Place: ", datafr_sub$place ) ) Z addPopups used to display info when it is click on the object.

STAT_HW-2

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