Homework help!

I need to show a complete solution, as well as explain the meaning of the confidence level?

A research was conducted to assess the impact of Netflix on students' academic performance. A random sample of 300 students resulted in a sample mean of 10.7 hours (watched per week) with a population standard deviation of 4.2 hours.

Calculate a 99 % confidence interval for the data (round your answer to 2 decimal places).

Confidence level indicates the possibility that the confidence interval can contain the population parameter ie it is the probability that the value of a parameter falls within a specified range of values.Some of the most common confidence levels are 90%,95% and 99%.In the given question 99% confidence interval indicates that we are 99% confident that most of these intervals contain the true population parameter ie we can expect that 99% of the interval estimates to include the population parameter.

For the given data,

the 99% confidence interval lies between 10.07 and 11.32

Lower bound = 10.7-0.62565 =10.07

Upper bound =10.7+0.62565 =11.32

The obtained result can be interpreted as we are 99% confident that the true population mean falls between the interval 10.07 and 11.32.

Step-by-step explanation

Given, mean, ?x?? ?? =10.7 hours

standard deviation, ?σ? =4.2 hours

n=300

For 99% CI,

1-?α? =0.99

?α?= 0.01

so,?α/2? =0.005

From the standard normal table,z_0.005 value or critical value =2.576 =2.58

so, CI =?x?? ?±? z_?α?/2 [?σ/(?n)? ]

CI =10.7?±? 2.58[4.2/?3?00? ]

CI =10.7?±? 2.58*0.2425

CI =10.7?±? 0.62565 = (10.07,11.32)