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Categorical Data

Grade 11 · Statistics · Worksheet 2

  1. Tane surveyed 60 students about their preferred type of music and whether they play an instrument. The results are: 15 play an instrument and prefer Rock, 12 play an instrument and prefer Pop, 9 play an instrument and prefer Jazz, 10 do not play an instrument and prefer Rock, 8 do not play an instrument and prefer Pop, and 6 do not play an instrument and prefer Jazz. Create a two-way frequency table summarizing this categorical data. Answer: ______________
  2. A medical researcher is studying the effectiveness of a new drug for reducing cholesterol levels. In a clinical trial with 180 patients, the mean reduction in LDL cholesterol was 28.4 mg/dL with a standard deviation of 7.2 mg/dL. The researcher wants to test if this reduction is significantly greater than the standard treatment's average reduction of 25 mg/dL. Using a significance level of α = 0.01, calculate the test statistic and determine whether there is sufficient evidence to support the claim that the new drug provides a greater reduction than the standard treatment.
    • A. z = 4.24, Reject H₀
    • B. z = 2.12, Fail to reject H₀
    • C. z = 6.36, Reject H₀
    • D. z = 3.18, Fail to reject H₀
  3. A survey was conducted at a high school to determine students' preferred music genre and their favorite subject. The data is summarized in the following two-way table: | | Math | English | Science | |--------------|------|---------|---------| | Rock | 15 | 9 | 21 | | Pop | 11 | 25 | 13 | | Hip-Hop | 7 | 17 | 19 | Complete the two-way frequency table by calculating the row totals, column totals, and the grand total. Then, based on the completed table, how many students prefer Pop music and also chose English as their favorite subject? Answer: ______________
  4. Noah surveyed 75 students about their preferred type of physical activity and whether they participate in team sports. The results are: 18 participate in team sports and prefer running, 12 participate in team sports and prefer swimming, 9 participate in team sports and prefer cycling, 15 do not participate in team sports and prefer running, 14 do not participate in team sports and prefer swimming, and 7 do not participate in team sports and prefer cycling. Create a two-way frequency table summarizing this categorical data. Answer: ______________
  5. Kaia surveyed 72 students about their preferred mode of transportation to school. The results were: 28 walk, 19 bike, 15 bus, and 10 car. Create a frequency table summarizing this categorical data. Answer: ______________
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Answer Key & Explanations

Categorical Data · Grade 11 · Worksheet 2

  1. Tane surveyed 60 students about their preferred type of music and whether they play an instrument. The results are: 15 play an instrument and prefer Rock, 12 play an instrument and prefer Pop, 9 play an instrument and prefer Jazz, 10 do not play an instrument and prefer Rock, 8 do not play an instrument and prefer Pop, and 6 do not play an instrument and prefer Jazz. Create a two-way frequency table summarizing this categorical data. Answer: 60 Solution: Set up a two-way table with rows 'Plays Instrument' and 'Does Not Play Instrument', and columns 'Rock', 'Pop', 'Jazz'. - Plays Instrument & Rock: 15 - Plays Instrument & Pop: 12 - Plays Instrument & Jazz: 9 - Does Not Play Instrument & Rock: 10 - Does Not Play Instrument & Pop: 8 - Does Not Play…
    Full step-by-step solution

    Step 1: Set up a two-way table with rows 'Plays Instrument' and 'Does Not Play Instrument', and columns 'Rock', 'Pop', 'Jazz'. Step 2: Fill in the given frequencies: - Plays Instrument & Rock: 15 - Plays Instrument & Pop: 12 - Plays Instrument & Jazz: 9 - Does Not Play Instrument & Rock: 10 - Does Not Play Instrument & Pop: 8 - Does Not Play Instrument & Jazz: 6 Step 3: Calculate row totals: - Plays Instrument total: 15 + 12 + 9 = 36 - Does Not Play Instrument total: 10 + 8 + 6 = 24 Step 4: Calculate column totals: - Rock total: 15 + 10 = 25 - Pop total: 12 + 8 = 20 - Jazz total: 9 + 6 = 15 Step 5: Grand total: 36 + 24 = 60, or 25 + 20 + 15 = 60. The completed two-way frequency table shows all frequencies and totals summing to 60 students.

  2. A medical researcher is studying the effectiveness of a new drug for reducing cholesterol levels. In a clinical trial with 180 patients, the mean reduction in LDL cholesterol was 28.4 mg/dL with a standard deviation of 7.2 mg/dL. The researcher wants to test if this reduction is significantly greater than the standard treatment's average reduction of 25 mg/dL. Using a significance level of α = 0.01, calculate the test statistic and determine whether there is sufficient evidence to support the claim that the new drug provides a greater reduction than the standard treatment. Answer: C. z = 6.36, Reject H₀ Solution: H₀: μ ≤ 25 mg/dL (new drug is not better than standard treatment) H₁: μ > 25 mg/dL (new drug provides greater reduction) z = (x̄ - μ) / (σ/√n) z = (28.4 - 25) / (7.2/√180) z = 3.4 / (7.2/13.4164) z = 3.4 / 0.5367 z = 6.36 For α = 0.01 in a right-tailed test, the critical z-value is 2.33 Since…
    Full step-by-step solution

    Step 1: State the hypotheses H₀: μ ≤ 25 mg/dL (new drug is not better than standard treatment) H₁: μ > 25 mg/dL (new drug provides greater reduction) Step 2: Calculate the test statistic z = (x̄ - μ) / (σ/√n) z = (28.4 - 25) / (7.2/√180) z = 3.4 / (7.2/13.4164) z = 3.4 / 0.5367 z = 6.36 Step 3: Determine the critical value For α = 0.01 in a right-tailed test, the critical z-value is 2.33 Step 4: Make a decision Since 6.36 > 2.33, we reject the null hypothesis Step 5: State the conclusion There is sufficient evidence at the 0.01 significance level to support the claim that the new drug provides a greater reduction in LDL cholesterol than the standard treatment. The correct answer is z = 6.36, Reject H₀.

  3. A survey was conducted at a high school to determine students' preferred music genre and their favorite subject. The data is summarized in the following two-way table: | | Math | English | Science | |--------------|------|---------|---------| | Rock | 15 | 9 | 21 | | Pop | 11 | 25 | 13 | | Hip-Hop | 7 | 17 | 19 | Complete the two-way frequency table by calculating the row totals, column totals, and the grand total. Then, based on the completed table, how many students prefer Pop music and also chose English as their favorite subject? Answer: 25 Solution: The table is already given with all cell values. The cell at the intersection of Pop (row) and English (column) is 25.
    Full step-by-step solution

    Step 1: The table is already given with all cell values. The cell at the intersection of Pop (row) and English (column) is 25. Step 2: This value represents the number of students who prefer Pop music and chose English as their favorite subject. The answer is 25.

  4. Noah surveyed 75 students about their preferred type of physical activity and whether they participate in team sports. The results are: 18 participate in team sports and prefer running, 12 participate in team sports and prefer swimming, 9 participate in team sports and prefer cycling, 15 do not participate in team sports and prefer running, 14 do not participate in team sports and prefer swimming, and 7 do not participate in team sports and prefer cycling. Create a two-way frequency table summarizing this categorical data. Answer: 75 Solution: Set up the two-way table structure with rows for team sports participation and columns for activity type. The completed two-way frequency table shows all frequencies and totals correctly sum to 75 students.
    Full step-by-step solution

    Step 1: Set up the two-way table structure with rows for team sports participation and columns for activity type. Step 2: Fill in the given joint frequencies: - Participates in Team Sports & Running: 18 - Participates in Team Sports & Swimming: 12 - Participates in Team Sports & Cycling: 9 - Does Not Participate in Team Sports & Running: 15 - Does Not Participate in Team Sports & Swimming: 14 - Does Not Participate in Team Sports & Cycling: 7 Step 3: Calculate row totals: - Participates in Team Sports total: 18 + 12 + 9 = 39 - Does Not Participate in Team Sports total: 15 + 14 + 7 = 36 Step 4: Calculate column totals: - Running total: 18 + 15 = 33 - Swimming total: 12 + 14 = 26 - Cycling total: 9 + 7 = 16 Step 5: Verify grand total: 39 + 36 = 75, or 33 + 26 + 16 = 75. The completed two-way frequency table shows all frequencies and totals correctly sum to 75 students.

  5. Kaia surveyed 72 students about their preferred mode of transportation to school. The results were: 28 walk, 19 bike, 15 bus, and 10 car. Create a frequency table summarizing this categorical data. Answer: Walk: 28, Bike: 19, Bus: 15, Car: 10 Solution: List the categories: Walk, Bike, Bus, Car. Walk: 28 Bike: 19 Bus: 15 Car: 10
    Full step-by-step solution

    Step 1: List the categories: Walk, Bike, Bus, Car. Step 2: Record the frequency for each category: - Walk: 28 students - Bike: 19 students - Bus: 15 students - Car: 10 students Step 3: Verify the total: 28 + 19 + 15 + 10 = 72 students. Step 4: The completed frequency table is: Walk: 28 Bike: 19 Bus: 15 Car: 10