Question

Name: LASS OF 2020 Hour: CLASS Which grade is more likely to go to prom? 202 Date: The student council at a large high school is wondering if Juniors or Seniors are more likely to attend Prom. They take a random sample of 50 Juniors and find that 28 are planning on attending Prom. They select a random sample of 45 Seniors and 29 are planning on attending. Hypotheses: Do the data provide convincing evidence that a higher proportion of Seniors are going to prom than Juniors? Use a 5% significance level.

STATE: Parameter: Statistic: Hypotheses: Significance Level:
PLAN: Name of procedure: Check Conditions:
DO: Mean: Standard Deviation: Picture: General Formula: Specific Formula: Work: Test Statistic: P-value:
CONCLUDE:
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Answer 1

Step-by-step explanation:

STATE:

Parameter of interest: Proportion of Juniors attending Prom (p1) and proportion of Seniors attending Prom (p2)

Statistic: Proportions from the random samples of Juniors and Seniors attending Prom

Hypotheses:

Null Hypothesis (H0): p1 = p2 (The proportion of Juniors attending Prom is equal to the proportion of Seniors attending Prom)

Alternative Hypothesis (HA): p2 > p1 (The proportion of Seniors attending Prom is higher than the proportion of Juniors attending Prom)

Significance Level: 0.05

PLAN:

Name of procedure: Two-sample z-test for proportions

Check Conditions:

Random Sampling: The samples are randomly selected, and both groups are less than 10% of the population size.

Independent Samples: The samples are independent, and the selection of Juniors for the sample does not affect the selection of Seniors.

Success-Failure Condition: Both sample sizes are greater than or equal to 10, and the expected number of successes and failures in both groups are greater than or equal to 5.

DO:

Mean: The difference in sample proportions: p2 - p1 = 29/45 - 28/50 = 0.2222

Standard Deviation: sqrt((p1*(1-p1)/n1) + (p2*(1-p2)/n2)) = sqrt((0.560.44/50) + (0.64440.3556/45)) = 0.122

Picture: This is a right-tailed test.

General Formula: (p2 - p1) - null value / standard error

Specific Formula: (0.2222 - 0) / 0.122 = 1.820

Test Statistic: The test statistic is 1.820.

P-value: Using a z-table or calculator, the p-value is 0.034.

CONCLUDE:

Since the p-value of 0.034 is less than the significance level of 0.05, we reject the null hypothesis. The data provide convincing evidence that a higher proportion of Seniors are going to prom than Juniors at this high school.