Questions: One Proportion Describe process: Probability of heads: Number of tosses: Number of repetitions: Show animation Draw Samples Choose statistic: Number of heads Proportion of heads Count samples As extreme as Count Proportion of repetitions: 24 / 500=0.0480 Options: Two-sided Exact Binomial Normal Approximation p-value =0.0339(z=1.83) Most recent results Number of Heads =19 Number of Tails =11

One Proportion

Describe process:
Probability of heads:
Number of tosses:
Number of repetitions:
Show animation
Draw Samples

Choose statistic:
Number of heads
Proportion of heads
Count samples
As extreme as
Count
Proportion of repetitions:
24 / 500=0.0480
Options:
Two-sided
Exact Binomial
Normal Approximation
p-value =0.0339(z=1.83)
Most recent results
Number of Heads =19
Number of Tails =11

Transcript text: One Proportion Describe process: Probability of heads: Number of tosses: Number of repetitions: Show animation Draw Samples Choose statistic: Number of heads Proportion of heads Count samples As extreme as $\square$ $\square$ Count Proportion of repetitions: $24 / 500=0.0480$ Options: Two-sided Exact Binomial Normal Approximation $p$-value $=0.0339(z=1.83)$ Most recent results Number of Heads $=19$ Number of Tails $=11$

Solution

Solution Steps

Step 1: Identify the Problem

The problem involves determining whether we have enough evidence to reject the null hypothesis (Ho: p = 0.5) based on the given data.

Step 2: Understand the Given Data

Probability of heads (p): 0.5
Number of tosses: 30
Number of heads: 19
Number of tails: 11
Number of repetitions: 500
Proportion of repetitions with heads ≥ 20: 24/500 = 0.0480
p-value: 0.0339 (z = 1.83)

Step 3: Analyze the p-value

The p-value is 0.0339, which is less than the common significance level of 0.05. This indicates that the observed result is statistically significant.