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A random sample of 16 grade 12 students was randomly selected and interviewed, and the number of private messages that they send daily was obtained. The null hypothesis is said to be rejected if the sample mean is at least 102; otherwise, the null hypothesis will be accepted. It is assumed that the number of text messages that a grade 12 student sends in a day follows a normal distribution with a standard deviation equal to 5 private messages. Compute the probability of committing a type I error.

A random sample of 16 grade 12 students was randomly selected and interviewed, and the number of private messages that they send daily was obtained. The null hypothesis is said to be rejected if the sample mean is at least 102; otherwise, the null hypothesis will be accepted. It is assumed that the number of text messages that a grade 12 student sends in a day follows a normal distribution with a standard deviation equal to 5 private messages. Compute the probability of committing a type I error.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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4. A researcher wants to test the following hypotheses: H: The average daily number of private messages that a grade 11 student sends is equal to 100. H: The average daily number of private messages that a grade 11 student sends is greater than 100. A random sample of 16 grade 12 students was randomly selected and interviewed, and the number of private messages that they send daily was obtained. The null hypothesis is said to be rejected if the sample mean is at least 102; otherwise, the null hypothesis will be accepted. It is assumed that the number of text messages that a grade 12 student sends in a day follows a normal distribution with a standard deviation equal to 5 private messages. Compute the probability of committing a type I error.
Transcribed Image Text:4. A researcher wants to test the following hypotheses: H: The average daily number of private messages that a grade 11 student sends is equal to 100. H: The average daily number of private messages that a grade 11 student sends is greater than 100. A random sample of 16 grade 12 students was randomly selected and interviewed, and the number of private messages that they send daily was obtained. The null hypothesis is said to be rejected if the sample mean is at least 102; otherwise, the null hypothesis will be accepted. It is assumed that the number of text messages that a grade 12 student sends in a day follows a normal distribution with a standard deviation equal to 5 private messages. Compute the probability of committing a type I error.
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