Statistics Chapter 5: Measures of Central Tendency
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Questions and Answers

What is the range of the repair cost?

  • $1
  • $2 (correct)
  • $0.50
  • $3

    • What is the correct sample variance for the weights provided?

  • 0.00156 grams²
  • 0.00389 grams² (correct)
  • 0.00225 grams²
  • 0.00400 grams²

    • What is the sample standard deviation for the weights of the candies?

  • 0.062 grams
  • 0.061 grams
  • 0.071 grams
  • 0.067 grams (correct)

    • Which histogram correctly represents the distribution of weights?

    <p>Histogram B</p> Signup and view all the answers

    How is the distribution of the weights characterized?

    <p>Skewed right</p> Signup and view all the answers

    What is the mean weight of the candies?

    <p>0.843 grams</p> Signup and view all the answers

    Which measure of central tendency is most appropriate for the weight of the candy?

    <p>Mean</p> Signup and view all the answers

    What can be concluded if the plotted values are not linear?

    <p>The relationship represented by the plotted values cannot be analyzed using linear regression.</p> Signup and view all the answers

    What does the boxplot indicate about outliers if there are no points outside of the 1.5(IQR) boundary?

    <p>There are no outliers present in the data.</p> Signup and view all the answers

    When constructing a 95% confidence interval to estimate the population mean cost, what is the implication of rounding to one decimal place?

    <p>The confidence interval will be less precise but simpler to interpret.</p> Signup and view all the answers

    If a simple random sample of size n = 10 is taken and variability in repair costs is evenly distributed, what would happen to the width of a 95% confidence interval compared to a larger sample?

    <p>It would be wider due to a smaller sample size.</p> Signup and view all the answers

    What can be said about the interpretation of a 95% confidence interval that is particularly wide?

    <p>It suggests high variability in the sample data used for estimation.</p> Signup and view all the answers

    What happens to the confidence level if we were to calculate a 99% confidence interval instead of a 95% confidence interval?

    <p>It would widen as we desire more certainty.</p> Signup and view all the answers

    When determining if there are outliers, what criterion is used if there are values beyond the first or third quartiles?

    <p>Values beyond $1.5 * IQR$.</p> Signup and view all the answers

    Why might a second random sample from the same population yield different results for the estimated mean cost of repair?

    <p>Sampling error could introduce variance.</p> Signup and view all the answers

    What is the point estimate for the population proportion of adults who believe that televisions are a luxury?

    <p>0.498</p> Signup and view all the answers

    Which requirement must be satisfied to construct a confidence interval for the population proportion?

    <p>10</p> Signup and view all the answers

    In a 95% confidence interval for the proportion who believe televisions are a luxury, which statement is correct?

    <p>We are 95% confident the proportion lies within the interval.</p> Signup and view all the answers

    If the 95% confidence interval for the luxury belief is found to be (0.450, 0.546), what does this suggest about a supermajority believing so?

    <p>It is highly unlikely since the upper bound is less than 0.60.</p> Signup and view all the answers

    What is the interpretation of a confidence interval result of (0.450, 0.546)?

    <p>We expect the true proportion of luxury-believers to fall within this range 95% of the time.</p> Signup and view all the answers

    What is the implication of the population proportion being estimated at 0.498?

    <p>Around half of the adults consider televisions a luxury.</p> Signup and view all the answers

    How does the sample size of 1029 affect the confidence interval's width?

    <p>A larger sample size decreases the width of the confidence interval.</p> Signup and view all the answers

    What is needed to determine the standard error for the proportion in constructing a confidence interval?

    <p>Sample proportion and sample size.</p> Signup and view all the answers

    What is the total number of entries in the data table?

    <p>11</p> Signup and view all the answers

    Which weight corresponds to the maximum total length recorded in the data table?

    <p>155 kg</p> Signup and view all the answers

    For a sample size of 15, what is the critical value for the correlation coefficient?

    <p>0.514</p> Signup and view all the answers

    If the correlation coefficient is less than -0.514 for a sample size of 15, what can be concluded?

    <p>The correlation is significant and negative.</p> Signup and view all the answers

    What does a larger z-score indicate for the weight of a baby born in week 34 compared to a baby born in week 40?

    <p>The baby born in week 34 weighs relatively more.</p> Signup and view all the answers

    Which of the following total lengths appears most frequently in the data table?

    <p>150.0 cm</p> Signup and view all the answers

    What is the correct interpretation of the first quartile (Q1)?

    <p>25% of the monthly returns fall below or equal to Q1.</p> Signup and view all the answers

    What range of weights is represented in the data table?

    <p>60 kg to 155 kg</p> Signup and view all the answers

    According to the correlation coefficients, what value would represent a weak correlation for a sample size of 12?

    <p>0.388</p> Signup and view all the answers

    Which of the following describes the second quartile (Q2)?

    <p>Q2 is equivalent to the median of the dataset.</p> Signup and view all the answers

    What does the third quartile (Q3) represent in terms of the dataset?

    <p>75% of the monthly returns fall below or equal to Q3.</p> Signup and view all the answers

    How many entries in the data table have a weight of 105 kg?

    <p>2</p> Signup and view all the answers

    What is the minimum total length recorded in the data table?

    <p>120.5 cm</p> Signup and view all the answers

    Which statement correctly describes outliers according to the given data?

    <p>Outliers represent values that are significantly different from the rest of the data.</p> Signup and view all the answers

    What critical value would indicate that a correlation is significant for a sample size of 25?

    <p>0.396</p> Signup and view all the answers

    Which of the following statements is not true regarding the interpretation of quartiles?

    <p>The third quartile indicates that 25% of the data is above it.</p> Signup and view all the answers

    Which option correctly represents the role of quartiles in identifying outliers?

    <p>Outliers can only exist outside the interquartile range.</p> Signup and view all the answers

    What is the main purpose of determining quartiles in data analysis?

    <p>To divide data into equal parts for analyzing distribution.</p> Signup and view all the answers

    How many pregnancies would be expected to last less than 210 days if 100 pregnant individuals were selected from the population?

    <p>36</p> Signup and view all the answers

    What is the expected number of samples with a mean of 210 days or less when selecting samples of size n = 18 from the population?

    <p>6</p> Signup and view all the answers

    If 100 independent samples of size n = 33 were obtained, how many samples would you expect to have a sample mean of 210 days or less?

    <p>2</p> Signup and view all the answers

    What is the expected number of different students who would read more than 94 words per minute from a sample of 100?

    <p>27</p> Signup and view all the answers

    What is the conclusion about a mean reading rate of 90.1 wpm given that its probability is 0.1679?

    <p>It is a typical result from the population.</p> Signup and view all the answers

    What is the confidence interval for the population mean number of books read?

    <p>12.34 to 14.06</p> Signup and view all the answers

    In the context of repair costs, what conclusion can be drawn regarding the plotted values?

    <p>The plotted values show a clear linear pattern.</p> Signup and view all the answers

    What is the upper bound of the confidence interval for the mean cost of repair?

    <p>$2484.3</p> Signup and view all the answers

    Study Notes

    • Observational studies measure the response variable without influencing the explanatory variable.
    • Designed experiments assign individuals to groups, change the explanatory variable, and record the response variable.
    • Designed experiments allow researchers to claim causation between variables.
    • Observational studies do not allow researchers to claim causation.
    • In an experiment, the researcher controls one variable to determine its effect on another variable.
    • Observational studies only observe/record the value of response variable.
    • A statistical summary of a sample is called a statistic.
    • A statistical summary of a population is called a parameter.
    • A quantitative variable is discrete if it can be counted (e.g., number of books).
    • A quantitative variable is continuous if it cannot be counted (e.g., weight).
    • The range of a data set is the difference between the largest and smallest values.
    • Sample variance is a measure of the spread of data around the mean.
    • Sample standard deviation is the square root of sample variance.
    • The linear correlation coefficient (r) measures the strength and direction of a linear association between two variables.
    • A positive correlation means that higher values of one variable tend to be associated with higher values of the other variable.
    • A negative correlation means that higher values of one variable tend to be associated with lower values of the other variable.
    • A scatter diagram displays the relationship between two variables.
    • A linear correlation coefficient of 1 or -1 indicates a perfect linear relationship.
    • Values of r close to 0 indicate a weak linear relationship.
    • Critical values of r determine if a linear relationship exists between two variables.
    • A p-value is the probability of observing a result as extreme or more extreme than the observed result, assuming the null hypothesis is true.
    • The null hypothesis is the statement that there is no effect or relationship between variables being studied.
    • The alternate hypothesis is the statement that there is an effect or relationship between variables being studied.

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    Description

    This quiz covers key concepts from Chapter 5 of statistics, focusing on measures of central tendency, variance, standard deviation, and confidence intervals. Evaluate your understanding of distributions, outliers, and implications of sample sizes. Test your knowledge on how to interpret various statistical representations related to repair costs and weights of candies.

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