Question

Polytechnic Institute Australia Marketing Services 2022 collected information from 300 students with an average used their smartphones in minutes per day is 195. The selected information is normally distributed with a mean of 180 minutes and a standard deviation of 30 minutes. Based on the given information, the value of the test statistic is: Type your answer rounding to 2 dp.

Answer 1

To conduct a hypothesis test in this scenario, calculate the test statistic using the formula provided. The value of the test statistic is approximately 0.25 when rounded to two decimal places.

Step-by-step explanation:

To conduct a hypothesis test for this scenario, we need to calculate the test statistic. The test statistic is the difference between the sample mean and the hypothesized population mean, divided by the standard error of the mean. In this case, the sample mean is 4.75 hours, and the hypothesized population mean is 4.5 hours. The standard error of the mean can be calculated by dividing the sample standard deviation by the square root of the sample size.

Using the given values: sample mean = 4.75 hours, sample standard deviation = 2.0 hours, and sample size = 15, the test statistic can be calculated as follows:

Test Statistic = (Sample Mean - Hypothesized Mean) / (Sample Standard Deviation / √(Sample Size))

Test Statistic = (4.75 - 4.5) / (2.0 / √15) ≈ 0.249 or approximately 0.25