if young men thought that their own level of muscle was about what women prefer, the mean "muscle gap" in the study would be 0. we suspect that young men think women prefer more muscle than they themselves have.
a)what is the value of he test statistic Z?
b)you can tell from the value of Z that the evidence in favor of the alternative is very strong(that is the p-value is very small). explain why this is true.
What level of significance is being used? Are you using a one-tailed or two-tailed test?
To find the value of the test statistic Z, we need more information about the study, such as the sample size, mean muscle level of young men, and the mean muscle level preferred by women. Please provide this information so we can calculate the Z-value accurately.
Regarding part b and the evidence in favor of the alternative, we can infer the strength of evidence by looking at the p-value associated with the test statistic Z. The p-value represents the probability of observing a test statistic as extreme or more extreme than the one observed if the null hypothesis were true.
In this case, the null hypothesis is that young men's perception of their own level of muscle is what women prefer. The alternative hypothesis is that young men think women prefer more muscle than they themselves have. If the p-value is very small, typically below a predetermined significance level (e.g., 0.05), it suggests strong evidence against the null hypothesis. The smaller the p-value, the stronger the evidence against the null hypothesis and in favor of the alternative.
To determine the p-value associated with the Z-value, we would need the sample size and other relevant information from the study. Once we have that information, we can conduct hypothesis testing and calculate the p-value using statistical software or tables.