In a test of the hypothesis that females smile at others more than males do, females and males were videotaped while interacting and the number of smiles emitted by each sex was noted. Using the following information regarding number of smiles in the five-minute interaction, examine whether there are sex differences in the number of smiles. Males FemalesN1 = 5 N2 = 5X1 = 7.6 X2 = 15.2S12 = 17.04 S22 = 8.96Which is the independent variable and which is the dependent variable?What is your research hypothesis?What is your null hypothesis?Which test should you use (Two Sample Independent t, ANOVA, Chi-square, or correlation )?Calculate the test statistic.interpret whether you have statistically significant results when α = .05.State whether the null hypothesis is rejected. Include critical region.Provide an overall sentence about the conclusion reached.

The objective of this question is to test the hypothesis that females smile more than males. We are given the sample size, mean, and variance for both males and females. We are asked to identify the independent and dependent variables, state the research and null hypotheses, identify the appropriate statistical test, calculate the test statistic, and interpret the results.The independent variable is the sex of the individuals (male or female) because it is the variable that we are manipulating or categorizing. The dependent variable is the number of smiles because it is the outcome that we are measuring.The research hypothesis is that females smile more than males. In statistical terms, this is H1: μ1 < μ2, where μ1 is the mean number of smiles for males and μ2 is the mean number of smiles for females.The null hypothesis is that there is no difference in the number of smiles between males and females. In statistical terms, this is H0: μ1 = μ2.Given that we have two independent groups (males and females) and we are comparing their means, the appropriate statistical test to use is the Two Sample Independent t-test.To calculate the test statistic, we use the formula for the t-statistic in a two-sample t-test: t = (X1 - X2) / sqrt[(S1^2/N1) + (S2^2/N2)]. Substituting the given values, we get: t = (7.6 - 15.2) / sqrt[(17.04/5) + (8.96/5)] = -7.6 / sqrt[3.408 + 1.792] = -7.6 / sqrt[5.2] = -7.6 / 2.28 = -3.33.The critical value for a two-tailed t-test with 8 degrees of freedom (N1 + N2 - 2) and α = .05 is approximately ±2.306. Since our calculated t-statistic of -3.33 is less than the critical value of -2.306, we reject the null hypothesis.In conclusion, we have statistically significant results at the α = .05 level, indicating that females do indeed smile more than males. The null hypothesis is rejected, supporting the research hypothesis that there is a difference in the number of smiles between males and females.The independent variable is the sex of the individuals and the dependent variable is the number of smiles. The research hypothesis is that females smile more than males and the null hypothesis is that there is no difference in the number of smiles between males and females. The appropriate statistical test is the Two Sample Independent t-test. The calculated t-statistic is -3.33, which is less than the critical value of -2.306, so we reject the null hypothesis. The results are statistically significant at the α = .05 level, indicating that females do indeed smile more than males.