Question

a sample of 106 middle student

1. A sample of 106 middle school students participated in a study about laptop use. The researchers reported that these students used their laptops for 13.2 minutes on average for taking notes with a standard deviation of 19.5 minutes. They want to use this information to infer about all the middle school students in the country. a. Define the target parameter in words and symbols. b. Calculate the 90% confidence interval for the target parameter and interpret. C. Explain what'90% confidence implies in your answer in part b.

Answer 1

a) Here our target parameter is Mu and it is the on an average use of laptop to taking notes.

b)

The provided sample mean is X = 13.2 and the sample standard deviation is s = 19.5. The size of the sample is n = 106 and the required confidence level is 90%. The number of degrees of freedom are df = 106 – 1 = 105, and the significance level is a = 0.1. Based on the provided information, the critical t-value for a = 0.1 and df = 105 degrees of freedom is te = 1.659. The 90% confidence for the population mean u is computed using the following expression c XS - TXO CI= (x y = + tema) Vn Therefore, based on the information provided, the 90 % confidence for the population mean u is CI = ( 13.2 – 1.659 x 19.5 129 (13.2 V106 1.659 x 19.5) V106 ) = (13.2 - 3.143, 13.2 + 3.143) = (10.057, 16.343) which completes the calculation.

c) We are 90% confident that the on an average time spent on laptop is the country is lies between 10.057 to 16.343.

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