Question

Gen Z and Smartphones-As part of Jody's research into the online habits of Gen Z students at MSU, she asks a random sample of 32 MSU Gen Z students how many hours per day they use their smartphone. She calculate a sample mean of 4.98 hours with a standard deviation of 1.748

Round all calculated values to 4 decimal places as appropriate.
Calculate a 10% confidence interval for the mean number of hours Gen 2 students at 14SU spend on their smartphones

Answer 1

To calculate a 10% confidence interval for the mean number of hours Gen Z students at MSU spend on their smartphones, you can use the formula: Confidence Interval = Sample Mean ± (Critical Value) × (Standard Deviation / Square Root of Sample Size). Plug in the values given and calculate the lower and upper bounds to find the confidence interval.

Step-by-step explanation:

To calculate a 10% confidence interval for the mean number of hours Gen Z students at MSU spend on their smartphones, we can use the formula:

Confidence Interval = Sample Mean ± (Critical Value) × (Standard Deviation / Square Root of Sample Size)

Given that the sample mean is 4.98 hours, the standard deviation is 1.748, and the sample size is 32, we can proceed with the calculations:

1. Find the critical value for a 10% confidence level. Since the sample size is large (n ≥ 30), we can use the Z-table. A 10% confidence level corresponds to a z-score of 1.645.
2. Plug in the values into the formula:
   Confidence Interval = 4.98 ± (1.645) × (1.748 / √32)
3. Calculate the confidence interval:
   Confidence Interval = 4.98 ± (1.645) × (1.748 / 5.656854)
4. Simplify the calculation:
   Confidence Interval = 4.98 ± (1.645) × (0.30927)
5. Calculate the lower bound:
   Lower Bound = 4.98 - (1.645 × 0.30927)
6. Calculate the upper bound:
   Upper Bound = 4.98 + (1.645 × 0.30927)

Therefore, the 10% confidence interval for the mean number of hours Gen Z students at MSU spend on their smartphones is (4.8644, 5.0956).