A quality control engineer at a semiconductor manufacturing plant collects data on the defect rate of 1,000 microchips. Which of the following actions fall under the domain of descriptive statistics? (Select all that apply)

Calculating the mean and standard deviation of the defect rate for the 1,000-chip sample.

Constructing a histogram to visualize the distribution of defects in the sample.

Using the sample defect rate to create a 95% confidence interval for the defect rate of the entire production run.

Concluding that a change in the manufacturing process has caused a statistically significant reduction in defects based on the sample.

A data scientist is analyzing user engagement on a new mobile application. The workflow involves collecting data from a sample of 5,000 users. Which of the following sequences represents a logically correct statistical workflow?

First, create a bar chart of user activity types and calculate the median session duration; then, use this sample data to generalize about the behavior of all application users.

First, use a t-test to infer if the average engagement time is greater than 10 minutes; then, calculate the sample mean and variance.

First, make a prediction about the churn rate for the next quarter; then, collect the sample data to verify the prediction.

First, use the sample to draw conclusions about the entire user population; then, present the sample data in tables and charts.

The temperature in degrees Celsius is measured by a sensor. This data is an example of which measurement scale, and why?

Interval, because the difference between 10°C and 20°C is the same as between 20°C and 30°C, but there is no true zero.

Nominal, because it categorizes temperature.

Ordinal, because 20°C is warmer than 10°C.

Ratio, because 20°C is twice as hot as 10°C.

An engineer measures the weight of a component in kilograms. This measurement is on a ratio scale because:

It has a true zero point, where 0 kg means no weight, and ratios like '20 kg is twice as heavy as 10 kg' are meaningful.

The values can be ordered from lightest to heaviest.

The difference between 10 kg and 20 kg is meaningful.

An engineering team is analyzing performance data from a set of electric motors. They have collected the following variables: (1) Motor model name, (2) Operating temperature in Kelvin, (3) Performance rating ('Low', 'Medium', 'High'), and (4) Year of manufacture. Which of the following statistical operations are valid for the given data types? (Select all that apply)

Calculating the ratio of the operating temperatures of two motors (e.g., Motor A is 1.5 times hotter than Motor B).

Calculating the median of the performance ratings.

Calculating the mean of the years of manufacture.

Calculating the average (mean) of the motor model names.

In a(n) ______________, researchers manipulate one or more variables to observe the effect on other variables, while in a(n) ______________, researchers measure characteristics without attempting to influence them.

controlled experiment; observational study

observational study; controlled experiment

case-control study; cohort study

A research team wants to determine if a new fertilizer causes an increase in crop yield. They divide a field into 100 plots, randomly assigning 50 plots to receive the new fertilizer and 50 plots to receive a standard fertilizer. They then compare the yields. What type of study is this?

A randomized controlled experiment

An epidemiologist studies the medical records of 1,000 individuals, 500 of whom have a rare disease (cases) and 500 who do not (controls), to identify past exposures that may be linked to the disease. This is an example of:

A case-control observational study

A study finds a strong positive association between the number of hours engineers spend using a new CAD software and their project completion speed. Which of the following conclusions are validly supported by this information alone? (Select all that apply)

There is a correlation between the hours spent on the new CAD software and project completion speed.

It is possible that faster engineers are more likely to adopt and use new software, and the software itself is not the cause of the speed increase.

Using the new CAD software causes engineers to complete projects faster.

The study must have been a randomized controlled experiment.

A pharmaceutical company wants to test the effectiveness of a new drug for reducing blood pressure. Which of the following study designs would provide the strongest evidence for a causal relationship between the drug and a reduction in blood pressure?

A randomized controlled trial where patients are randomly assigned to receive either the new drug or a placebo, with neither the patients nor the researchers knowing who received which.

An observational study tracking 5,000 patients who are already taking the drug and comparing their outcomes to the general population.

A case-control study identifying patients with low blood pressure and looking at their past medication history.

A survey asking doctors for their opinions on the effectiveness of the new drug.

An engineer is tasked with assessing the overall quality of a large shipment of 100,000 resistors, which are packaged in 1,000 boxes of 100 resistors each. The engineer has limited time and budget. Which of the following sampling strategies represent a valid trade-off between logistical feasibility and statistical principles? (Select all that apply)

Randomly select 20 boxes (clusters) and then test every resistor within those 20 boxes.

Assign a number to every single one of the 100,000 resistors and draw 2,000 unique random numbers to identify which resistors to test.

Select the first 10 boxes from the top of the shipment and test all resistors inside them, as this is the quickest method.

Test all resistors from the 5 boxes located closest to the loading dock door.

A political pollster conducts a survey by calling landline telephones. This method may introduce which type of error because it excludes people who only use mobile phones or have no phone at all?

Coverage error (or sample frame error)

A web-based survey on internet usage habits is advertised on a tech news website. The results are likely to be skewed because only people who are interested in technology and visit that specific site will participate. This is a classic example of:

Selection error (or self-selection bias)

A research firm conducts a large-scale survey with 50,000 respondents to predict consumer preference for a new product. The survey is administered only via an online platform, and the link is promoted on social media. Despite the very large sample size leading to a small margin of error, the prediction turns out to be highly inaccurate. Which of the following are plausible explanations for this failure? (Select all that apply)

The study suffered from coverage error, as it excluded individuals who are not active on social media or lack internet access.

The large sample size magnified the effect of a systematic bias in the sampling method.

The study suffered from selection bias, as individuals with a strong interest in the product category were more likely to participate.

The random sampling error was too large due to the sample size.

Which of the following scenarios describes a non-sampling error? (Select all that apply)

A survey question is worded ambiguously, leading respondents to interpret it in different ways and provide inaccurate answers.

A data entry clerk accidentally transposes digits while recording measurements from a lab notebook into a spreadsheet.

In a telephone survey, a significant number of individuals selected for the sample refuse to participate.

A researcher uses a well-calibrated instrument, but by chance, the 20 components selected for a sample have a slightly higher average weight than the entire population of components.

A random variable is:

A function assigning numerical values to outcomes

What does the standard deviation of a dataset measure?

The average spread or dispersion of data points around the mean.

The total sum of all data points.

The average distance of each data point from the median.

The difference between the maximum and minimum values.

If a student's exam score is at the 85th percentile, what does this mean?

The student scored better than or equal to 85% of the other test-takers.

The student answered 85% of the questions correctly.

Only 15% of students scored higher than this student.

The student's score is 85% higher than the average score.

MCSE Quiz 1

Authored by ANUSHRUTH Batch

Mathematics

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which of the following is the primary goal of descriptive statistics?

To test a hypothesis about a population parameter.

To make predictions about future outcomes based on sample data.

To organize, summarize, and present the main features of a dataset.

To determine the causal relationship between two variables.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What type of data is the number of active users on a website?

Continuous

Categorical

Discrete

Ordinal

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which variable type best describes 'operating system type'?

Quantitative

Qualitative

Continuous

Interval

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which of the following is an example of qualitative data?

Height

Age

Gender

Weight

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which sampling method ensures representation from all strata of a population?

Simple random sampling

Cluster sampling

Stratified sampling

Systematic sampling

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which of the following is NOT a source of sampling error?

Random variation

Non-response bias

Sampling frame errors

Increasing sample size

MULTIPLE SELECT QUESTION

30 sec • 2 pts

Which of the following are types of statistics? (Select all that apply)

Descriptive

Inferential

Analytical

Computational

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MCSE Quiz 1

Which of the following is the primary goal of descriptive statistics?

What type of data is the number of active users on a website?

Which variable type best describes 'operating system type'?

Which of the following is an example of qualitative data?

Which sampling method ensures representation from all strata of a population?

Which of the following is NOT a source of sampling error?

Which of the following are types of statistics? (Select all that apply)

An engineer calculates the average tensile strength of 50 steel rods from a production batch. This single calculated average value is an example of:

A market analyst uses poll data from a sample of 1,200 voters to predict the outcome of a national election. This is an application of:

A quality control engineer at a semiconductor manufacturing plant collects data on the defect rate of 1,000 microchips. Which of the following actions fall under the domain of descriptive statistics? (Select all that apply)

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