A statistics student hands each of 300 classmates 2 cookies side by side on a plate. Of the 300 students, 171 choose the cookie that’s on their right hand side, and the remaining 129 choose the cookie that’s on their left. The student says, “That’s just like tossing a coin.” The student’s friend says, “No, it’s not.” Help them settle their argument by performing a one-sample z test in Problems 7-9.
I think it will be
1,78%
then confirm if that was the correct answer
Thanks youre right bud!
To settle the argument and perform a one-sample z test, we need to compare the observed distribution (where 171 students chose the cookie on their right and 129 students chose the cookie on their left) with the expected distribution (where we assume there is no preference and each student has a 50% chance of choosing either cookie).
Here are the steps to perform a one-sample z test for this problem:
Step 1: Define the null and alternative hypotheses:
- Null hypothesis (H0): The observed distribution is the same as the expected distribution (no preference).
- Alternative hypothesis (Ha): The observed distribution is different from the expected distribution (there is a preference).
Step 2: Calculate the test statistic:
We will use the formula for the z test statistic:
z = (p̂ - p0) / sqrt(p0 * (1 - p0) / n)
Where:
- p̂ is the observed proportion of students choosing the cookie on the right (171/300 = 0.57)
- p0 is the expected proportion of students choosing the cookie on the right (0.50)
- n is the sample size (300)
Step 3: Determine the critical value:
We need to specify the desired level of significance to find the critical value. Let's assume a significance level of 0.05, which corresponds to a 95% confidence interval. We'll use a standard normal distribution table to find the critical z-values. For a two-tailed test, we need to divide the significance level by 2. Hence, α/2 = 0.025.
Step 4: Calculate the p-value:
The p-value is the probability of observing a test statistic as extreme as or more extreme than the one calculated under the null hypothesis. We'll use a standard normal distribution table to find the p-value.
Step 5: Make a decision:
- If the test statistic falls within the critical region or if the p-value is less than the significance level, we reject the null hypothesis.
- If the test statistic falls outside the critical region or if the p-value is greater than the significance level, we fail to reject the null hypothesis.
Step 6: Interpret the results:
If we reject the null hypothesis, it means that there is evidence to suggest that there is a preference for one side of the cookie. If we fail to reject the null hypothesis, it means that there is not enough evidence to suggest a preference.
Performing this test will help settle the argument between the two students and determine if there is a significant preference for choosing one side of the cookie.