The null hypothesis, denoted as H₀, states that the population mean (μ) of the "like" ratings of male dates made by female dates is less than 8.00. The alternative hypothesis, denoted as H₁, contradicts the null hypothesis and suggests that the population mean is greater than 8.00.
To determine the test statistic, we need to calculate the t-value. The formula for the t-value is:
t = (x - μ) / (s / √n),
where x is the sample mean, μ is the population mean, s is the standard deviation, and n is the sample size.
Given the summary statistics n=199, x=7.89, and α=0.05 (significance level), we can calculate the test statistic.
First, we need to calculate the standard deviation. Unfortunately, the standard deviation (x₁.₉₂) is not provided, so we cannot compute the test statistic without it.
In summary, we cannot determine the test statistic without the standard deviation. To evaluate the original claim, we would need more information or the correct standard deviation to proceed with the hypothesis test.