If two populations are independent and each normally distributed and the population standard deviations are not equal, the test statisticT=X¯1−X¯2−(μ1−μ2)S21n1+S22n2‾‾‾‾‾‾‾‾√𝑇=𝑋¯1−𝑋¯2−(𝜇1−𝜇2)𝑆12𝑛1+𝑆22𝑛2 follows a:Question 4Select one:a.t-distribution with n1+n2−2 degrees of freedomt-distribution with 𝑛1+𝑛2−2 degrees of freedom b.standard normal distribution with n1+n2−2 degrees of freedomstandard normal distribution with 𝑛1+𝑛2−2 degrees of freedom c.t-distribution with degrees of freedom equal to (S21n1+S22n2)2(S21/n1)2n1−1+(S22/n2)2n2−1t-distribution with degrees of freedom equal to (𝑆12𝑛1+𝑆22𝑛2)2(𝑆12/𝑛1)2𝑛1−1+(𝑆22/𝑛2)2𝑛2−1 d.t-distribution with n−1 degrees of freedom

We wish to conduct a hypotheses test of the formH0: μ1 - μ2 = 0 vs H0: μ1 - μ2 > 0Both populations are assumed normal with equal variance. We draw 15 observations for the first sample and 12 observations for the second sample. State the distribution of the test statistic for the test.Question 1Select one:a.t-distribution with 26 degrees of freedomb.t-distribution with 27 degress of freedomc.t-distribution with 25 degrees of freedomd.normal distribution with 25 degrees of freedomClear my choice

The t distribution approaches the standardised normal distribution when the number of degrees of freedom increases.Question 14Select one:a.Falseb.True

Two Independent simple random samples are taken to test the difference between the means of two populations. The standard deviations are not known, but are assumed to be equal. The sample sizes are n1 = 15 and n2 = 35. The correct distribution to use is the t distribution with 51 degrees of freedom z distribution with 50 degrees of freedom z distribution with 49 degrees of freedom t distribution with 48 degrees of freedom

The t test for the difference between the means of two independent populationsalways assumes that the respectivea. sample sizes are equalb. sample variances are equalc. populations are normally distributed if each sample size is less than 30d. All of the above

Which of these is not an assumption of the two-sample t-test?Question 3Answera.Independenceb.Homogeneity of variancec.Normalityd.Sphericity