Need help on Number 20 19. If other factors are held constant, explain how each ofthe following influences the value of the independent-measures t statistic, the likelihood of rejecting thenull hypothesis, and the magnitude of measures of22effect size.a. Increasing the number of scores in each sample.b. Increasing the variance for each sample.As noted on page 304, when the two populationmeans are equal, the estimated standard error for theindependent-measures t test provides a measure ofhow much difference to expect between two samplemeans, For each of the following situations, assumeu, and calculate how much differencethat u, = Hzshould be expected between the two sample means.a. One sample has n = 6 scores with SS = 75 and thesecond sample has n = 10 scores with SSb. One sample has n =second sample has n = 10 scores with SS = 530.c. In part b, the samples have larger variability (biggerSS values) than in part a, but the sample sizes areunchanged. How does larger variability affect themagnitude of the standard error for the sample%3D135.6 scores with SS = 310 and the23mean difference?21. Two samples are selected from the same population. Forcach of the following, calculate how much duference isexpected, on average, between the two sample means.a. One sample has nthe pooled variance is 60.D. One sample has n = 12, the second has n=D.and the pooled variance is 60.c. In part b, the sample sizes are larger but the pooledvariance is unchanged. How does larger sample4, the second has e 6, and 304CHAPTER 10 | The t Test for Two Independent SamplesThe independent-measures t uses the difference between two sample means to evaluate ahypothesis about the difference between two population means. Thus, the independent-measures t formula is(M,- M,) - (H, - H.)sample mean difference – population mean differenceestimated standard errorS(M-M)In this formula, the value of M, - M, is obtained from the sample data and the value fo.u, - H, comes from the null hypothesis. In a hypothesis test, the null hypothesis sets thepopulation mean difference equal to zero, so the independent measures t formula can hasimplified further,sample mean differencet =estimated standard errorIn this form, the t statistic is a simple ratio comparing the actual mean difference (numera-tor) with the difference that is expected by chance (denominator).The Estimated Standard Error In each of the t-score formulas, the standard error inthe denominator measures how accurately the sample statistic represents the populationparameter. In the single-sample t formula, the standard error measures the amount of errorexpected for a sample mean and is represented by the symbol s, For the independent-measures t formula, the standard error measures the amount of error that is expected whenyou use a sample mean difference (M, - M,) to represent a population mean difference(, - ,). The standard error for the sample mean difference is represented by the symbolS м-мм"Caution: Do not let the notation for standard error confuse you. In general, standard errormeasures how accurately a statistic represents a parameter. The symbol for standaraWhen the statistic is a sample mean, M, the symbol for standardFor the independent-measures test, the statistic is a sample mean differenceerror takes the form sstatisticerror isSM(M, - M,), and the symbol for standard errortells how much discrepancy is reasonable to expect between the sample statistic and tiecorresponding population parameter.isS (M-M)In each case, the standard errorInterpreting the Estimated Standard Error The estimated standard error of M,M, that appears in the bottom of the independent-measures t statistic can be interpretedin two ways. First, the standard error is defined as a measure of the standard or averagedistance between a sample statistic (M, - M,) and the corresponding population parameter(, - ,). As always, samples are not expected to be perfectly accurate and the standarderror measures how much difference is reasonable to expect between a sample statistic andthe population parameter.When the null hypothesis is true, however, the population mean difference is zero. Inthis case, the standard error is measuring how far, on average, the sample mean differenceis from zero. However, measuring how far it is from zero is the same asmeasuring howbig it is. Therefore, when the null hypothesis is true, the standard error is measuring howbig, on average, the sample mean difference is. Thus, there are two ways to interpetheestimated standard error of (M, – M,).1. It measures the standard distance between (M, – M,) and (u, - H2).2. It measures the standard, or average size of (M. – M) if the null hypothhesThat is, it measures how much difference is reasonable to expect between the twosample means.

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Need help on Number 20 19. If other factors are held constant, explain how each ofthe following influences the value of the independent-measures t statistic, the likelihood of rejecting thenull hypothesis, and the magnitude of measures of22effect size.a. Increasing the number of scores in each sample.b. Increasing the variance for each sample.As noted on page 304, when the two populationmeans are equal, the estimated standard error for theindependent-measures t test provides a measure ofhow much difference to expect between two samplemeans, For each of the following situations, assumeu, and calculate how much differencethat u, = Hzshould be expected between the two sample means.a. One sample has n = 6 scores with SS = 75 and thesecond sample has n = 10 scores with SSb. One sample has n =second sample has n = 10 scores with SS = 530.c. In part b, the samples have larger variability (biggerSS values) than in part a, but the sample sizes areunchanged. How does larger variability affect themagnitude of the standard error for the sample%3D135.6 scores with SS = 310 and the23mean difference?21. Two samples are selected from the same population. Forcach of the following, calculate how much duference isexpected, on average, between the two sample means.a. One sample has nthe pooled variance is 60.D. One sample has n = 12, the second has n=D.and the pooled variance is 60.c. In part b, the sample sizes are larger but the pooledvariance is unchanged. How does larger sample4, the second has e 6, and 304CHAPTER 10 | The t Test for Two Independent SamplesThe independent-measures t uses the difference between two sample means to evaluate ahypothesis about the difference between two population means. Thus, the independent-measures t formula is(M,- M,) - (H, - H.)sample mean difference – population mean differenceestimated standard errorS(M-M)In this formula, the value of M, - M, is obtained from the sample data and the value fo.u, - H, comes from the null hypothesis. In a hypothesis test, the null hypothesis sets thepopulation mean difference equal to zero, so the independent measures t formula can hasimplified further,sample mean differencet =estimated standard errorIn this form, the t statistic is a simple ratio comparing the actual mean difference (numera-tor) with the difference that is expected by chance (denominator).The Estimated Standard Error In each of the t-score formulas, the standard error inthe denominator measures how accurately the sample statistic represents the populationparameter. In the single-sample t formula, the standard error measures the amount of errorexpected for a sample mean and is represented by the symbol s, For the independent-measures t formula, the standard error measures the amount of error that is expected whenyou use a sample mean difference (M, - M,) to represent a population mean difference(, - ,). The standard error for the sample mean difference is represented by the symbolS м-мм&#34;Caution: Do not let the notation for standard error confuse you. In general, standard errormeasures how accurately a statistic represents a parameter. The symbol for standaraWhen the statistic is a sample mean, M, the symbol for standardFor the independent-measures test, the statistic is a sample mean differenceerror takes the form sstatisticerror isSM(M, - M,), and the symbol for standard errortells how much discrepancy is reasonable to expect between the sample statistic and tiecorresponding population parameter.isS (M-M)In each case, the standard errorInterpreting the Estimated Standard Error The estimated standard error of M,M, that appears in the bottom of the independent-measures t statistic can be interpretedin two ways. First, the standard error is defined as a measure of the standard or averagedistance between a sample statistic (M, - M,) and the corresponding population parameter(, - ,). As always, samples are not expected to be perfectly accurate and the standarderror measures how much difference is reasonable to expect between a sample statistic andthe population parameter.When the null hypothesis is true, however, the population mean difference is zero. Inthis case, the standard error is measuring how far, on average, the sample mean differenceis from zero. However, measuring how far it is from zero is the same asmeasuring howbig it is. Therefore, when the null hypothesis is true, the standard error is measuring howbig, on average, the sample mean difference is. Thus, there are two ways to interpetheestimated standard error of (M, – M,).1. It measures the standard distance between (M, – M,) and (u, - H2).2. It measures the standard, or average size of (M. – M) if the null hypothhesThat is, it measures how much difference is reasonable to expect between the twosample means.

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