Question

In: Statistics and Probability

A goal of financial literacy for children is to learn how to manage money wisely. One...

A goal of financial literacy for children is to learn how to manage money wisely. One question is: How much money do children have to manage? A recent study by Schnur Educational Research Associates randomly sampled 15 children between 8 and 10 years old and 18 children between 11 and 14 years old and recorded their monthly allowance. Is it reasonable to conclude that the mean allowance received by children between 11 and 14 years is more than the allowance received by children between 8 and 10 years? Use the 0.01 significance level. What is the p-value?

8–10 Years 11–14 Years 8–10 Years 11–14 Years
26 49 26 41
33 44 25 38
30 42 27 44
26 38 29 39
34 39 34 50
26 41 32 49
27 39 41
27 38 42
30 38 30

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  1. State the decision rule: H0: μ8-10 Year oldsμ11-14 Year oldsH1: μ8-10 Year olds <μ11-14 Year olds. (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)

  1. Compute the value of the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)

Solutions

Expert Solution

a. H0: The children between 8 - 10 years old received equal monthly allowance to childeren between 11-14 years old i.e. μ8-10 Year olds = μ11-14 Year olds

H1: The children between 8 - 10 years old received less monthly allowance to childeren between 11-14 years old

μ8-10 Year olds < μ11-14 Year olds

 > Age8_10 = c(26,33,30,26,34,26,27,27,30,26,25,27,29,34,32) > Age11_14 = c(49,44,42,38,39,41,39,38,38,41,38,44,39,50,49,41,42,30) > t.test(Age8_10,Age11_14,alternativr = "greater",conf.level = 0.99)     Welch Two Sample t-test data: Age8_10 and Age11_14 t = -8.8587, df = 29.516, p-value = 8.2e-10 alternative hypothesis: true difference in means is not equal to 0 99 percent confidence interval: -16.282678 -8.561766 sample estimates: mean of x mean of y 28.80000 41.22222 

the p- value is 8.2e-10 < 0.01, so we reject the null hypothesis and conclude that 11-14 years old received more allowance as compare to 8-10

test statistic is -8.858


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