Final answer:
The question is about determining whether a t-value falls within a specified range based on research prices of cell phones. It requires knowledge of hypothesis testing, calculation of p-values, and construction of confidence intervals, which are statistical concepts typically taught at the college level.
Step-by-step explanation:
When analyzing the research prices of cell phones to see if a t-value falls within a certain range, we are discussing a topic in Mathematics, specifically within the area of statistics. This involves hypothesis testing and confidence interval calculations, which are pertinent to college-level coursework.
In the case of the cell phone manufacturer believing the proportion of American adults owning cell phones is lower than 92%, we set up a hypothesis test. The null hypothesis (H0) would state there is no difference from the 92% expectation, while the alternative hypothesis (Ha) suggests that the proportion is indeed lower. With 174 of 200 surveyed adults having cell phones, we calculate a p-value to determine the statistical significance. If this p-value is less than the level of significance (0.05), we reject the null hypothesis.
Finding a 98% confidence interval for the population mean or proportion involves using given statistics like the population mean ($431.61), the sample mean, the sample standard deviation and the sample size to construct a range that we are 98% confident contains the true population means or proportion. Type I and Type II errors relate to the potential mistakes in hypothesis testing - rejecting a true null hypothesis or failing to reject a false null hypothesis, respectively.