Assume that the birthweights of babies born into low socioeconomic status are normally distributed with a mean of 116 oz and a standard deviation of 18 oz. We generate 100 random samples, each consisting of 100 birthweights from this distribution. For each sample, the hypothesesH0: µ = 120H1: µ < 120are posed for the appropriate one-tailed t-test at a 5% level of significance. Consider the number of samples k where H0 is accepted.Calculate the population mean and variance for k. (Hint: what does it mean to accept H0 for this data?)

Name: Assume that the birthweights of babies born into low socioeconomic sta
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Description: Assume that the birthweights of babies born into low socioeconomic status are normally distributed with a mean of 116 oz and a standard deviation of 18 oz. We generate 100 random samples, each consisting of 100 birthweights from this distribution. Fo

Given Information : Assume that the birthweights of babies born into low socioeconomic status are normally distributed with a mean of 116 oz and a standard deviation of 18 oz. We generate 100 random samples, each consisting of 100 birthweights from this distribution. Stated Hypothesis : H0 : µ = 120 v/s H1 : µ < 120 The provided sample mean is X¯=116 and the sample standard deviation is s=18, and the sample size is n=100. This corresponds to a left-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used. Rejection Region Based on the information provided, the significance level is \alpha = 0.05α=0.05, and the critical value for a left-tailed test is tc=−1.66. The rejection region for this left-tailed test is R = {t: t < -1.66}R=t:t<−1.66 Test Statistics The t-statistic is computed as follows: Decision about the null hypothesis Since it is observed that t=−2.222<tc=−1.66, it is then concluded that the null hypothesis is rejected. Using the P-value approach: The p-value is p=0.0143, and sincep = 0.0143 < 0.05p=0.0143<0.05, it is concluded that the null hypothesis is rejected. Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean μ is less than 120, at the 0.05 significance level.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Assume that the birthweights of babies born into low socioeconomic status are normally distributed with a mean of 116 oz and a standard deviation of 18 oz. We generate 100 random samples, each consisting of 100 birthweights from this distribution. For each sample, the hypotheses

H0	: µ = 120
H1	: µ < 120

are posed for the appropriate one-tailed t-test at a 5% level of significance. Consider the number of samples k where H0 is accepted.

Calculate the population mean and variance for k. (Hint: what does it mean to accept H0 for this data?)

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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