Boys of a certain age have a mean weight of 85 pounds. A complaint is made that

Question

Boys of a certain age have a mean weight of 85 pounds. A complaint is made that in a municipal children's home the boys are underfed As one bit of evidence, 25 of these boys are weighed and found to have a mean weight of 80.94 pounds and a sample standard deviation of 11 6 pounds. Is the complaint legitimate? Conduct a hypothesis test at significance level of 05 what is the P-value? 1. between 025 and.05 2 between 05 and 1 3 between 005 and 01 4 between 01 and 025 An ideal weight of a person is 60 kg The mean weight of the sample of 100 persons from the Assume that sigma 10 kg and a: 05 What is a Type l error for the appropriate hypothesis test? 1. We conclude that Honolulu Heart Study is 64 kg Are the people in the Honolulu study the mean weight of people in the Honolulu Heart study is more than 64 kg, when in fact it isn't 2. We conclude that the mean weight of people in the Honolulu Heart study is not more than 60 kg, when in fact it is 3. We conclude that the weight of people in the Honolulu Heart study is not more than 64 kg. when in fact it is 4. We conclude that the mean weight of people in the Honolulu Heart study is more than 60 kg. when in fact it isn't In a hypothesis test if the significance level is 05 and the P-value is 01, you should 1. both reject and reject the null hypothesis 2. reject the null hypothesis 3. can't make a conclusion 4. not reject the null hypothesis

Explanation / Answer

10. State the hypothesis. The null and alternative hypotheses are as follows:

H0:mu=85 (boys of certain age have mean weight of 85 pounds)

H1:mu<85 (boys of certain age have mean weight less than 85 pounds)

Assumptions: Sample size is small (n<30) and population standard deviation is unknown. Boys were sampled from randomized survey and it is assumed that histogram of their weight is roughly normal. The randomization condition and nearly normal conditions are met, use t model with (n-1)=925-10=24 degrees of freedom to do an one-sample t test for mean.

Test statistic.

t=(xbar-mu)/(s/sqrt n), where, xbar is sample mean, mu is population mean, s is sample standard deviation, and n is sample size.

=(80.94-85)/(11.6/sqrt 25)

=-1.75

Look for left most column (df=24) in the t table and then across df=24 locate the two values between which |t| falls. The two values are 1.711 and 2.064. Now note the one-tail probabilities (the test is left tailed) associated with these values, that is middle row of the three header rows. Thus the p value is represented as 0.025<p<0.05. Option 1. The rest of the options are therefore incorrect.

11. The null and alternative hypotheses are as follows:

H0:mu=60 (ideal weight of a person is 60 kg)

H1:mu>60 (ideal weight of a person is more than 60 kg)

The Type I error refer to incorrect rejection of true null hypothesis. Thus, one would commit Type I error if one concldes that ideal weight of a person is more than 60 kg, when actually it is 60 kg. Therefore, the correct option is 4. Going by definition only, one can discards options 1, 2 and 3.

12. Per rejection rule based on null hypothesis, one can reject null hypothesis if the p value is less than alpha=0.05. Here, p value (0.01) is less than 0.05, therefore, reject null hypothesis. Option 1 and 3 are not feasible, and option 4 is wrong. Thus, option 2 is right.

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