Claim: The majority of adults like pizza.

A sample of 400 randomly selected adults shows that 220 of them like pizza.
Based on the given sample information, do you think that the above claim is true? Why or why not?

I tend to think it is true since 220/400 is more than 50% and it was a random sample. If a sample is truly random that we can consider it to be representative of the population.

If they had asked people coming out of a pizza shop, then I would say no.

To determine whether the given claim that the majority of adults like pizza is true based on the sample information, we can conduct a hypothesis test.

Step 1: Set up the null and alternative hypotheses:
Null hypothesis (H₀): The proportion of adults who like pizza is equal to or less than 0.5 (i.e., 50% or less).
Alternative hypothesis (H₁): The proportion of adults who like pizza is greater than 0.5 (i.e., more than 50%).

Step 2: Calculate the test statistic:
In this case, we are comparing a sample proportion to a hypothesized proportion (0.5 or 50%). To calculate the test statistic, we can use the formula for a one-sample proportion test:

test statistic (Z) = (sample proportion - hypothesized proportion) / standard error

The sample proportion calculated from the given information is: p̂ = 220/400 = 0.55 (or 55%)
The standard error can be calculated using the formula: standard error = √(p̂(1-p̂)/n)
Where n is the sample size.

standard error = √(0.55(1-0.55)/400) ≈ 0.025

test statistic (Z) = (0.55 - 0.5) / 0.025 ≈ 2

Step 3: Determine the p-value:
The p-value is the probability of obtaining a test statistic as extreme as the one observed, assuming the null hypothesis is true. We can use a standard normal distribution table or statistical software to find the p-value corresponding to the test statistic.

For a one-tailed test with a test statistic of 2, the p-value is approximately 0.0228 (using a standard normal distribution table).

Step 4: Compare the p-value to the significance level:
The significance level (usually denoted as α) is the threshold below which we reject the null hypothesis. Commonly used values for α are 0.05 or 0.01.

If the p-value is less than the significance level, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

Step 5: Make a conclusion:
In this case, if we choose a significance level of 0.05 (5%), the p-value of 0.0228 is less than 0.05. Therefore, we reject the null hypothesis.

Conclusion:
Based on the given sample information, we have evidence to suggest that the claim that the majority of adults like pizza (proportion > 0.5) is true. The sample proportion of 0.55 is significantly higher than the hypothesized proportion of 0.5.