Final answer:
The mean times provided in options a.) (177.64, 192.36) and b.) (177.79, 192.21) are accurate estimates for the mean time students spend on physical activity each week, while option c.) (53.634, 62.366) is not a valid estimate as it doesn't match the unit of measurement provided. The exact interval cannot be selected without additional information on the confidence level. Therefore, the correct answer is:b.) (177.79, 192.21)
Step-by-step explanation:
The objective is to estimate the mean time students spend engaged in physical activity each week given a sample of 58 students with an average of 185 minutes and a standard deviation of 28 minutes. To achieve this, we can use a confidence interval.
Looking at the provided options a.) (177.64, 192.36), b.) (177.79, 192.21), and c.) (53.634, 62.366), the correct estimate of the mean time should be expressed in minutes, since the average and standard deviation are given in minutes. Therefore, options a and b are valid estimates as they reflect this unit correctly. Option c is incorrect due to the values being too small and not consistent with the other data provided.
With the provided data, we can't definitively determine which confidence interval is correct without knowing the confidence level or the calculation methodology used. However, options a and b are both reasonable based on the sample mean provided. The slight differences between these intervals would depend on the exact confidence level used and any rounding applied to the calculations.