A researcher believes a new diet should improve weight gain.To test his hypothesis a random sample of 10 people on the old diet and an independent random sample of 10 people on the new diet were selected.The selected people on the old diet gain an average of 5 pounds with a standard deviation of 2 pounds, while the average gain for selected people on the new diet was 8 pounds with a standard deviation of 1.5 pounds.Assume that the values are normally distributed in each population and that the population variances are approximately equal.Using$\alpha$= 0.05, the observed t value for this test is _______.
A)-1.96
B)-1.645
C)-2.100
D)-3.79
E)-1.734

Question

Quizplus · Accepted Answer

To find the observed t value for comparing the means of two independent samples with assumed equal variances, we use the formula for the t statistic in a two-sample t-test. The formula is:$$ t = \frac{(\bar{x}_1 - \bar{x}_2)}{\sqrt{s_p^2(\frac{1}{n_1} + \frac{1}{n_2})}} $$where $\bar{x}_1$ and $\bar{x}_2$ are the sample means, $s_p^2$ is the pooled variance, and $n_1$ and $n_2$ are the sample sizes. Given that the sample sizes are equal and the variances are approximately equal, we can calculate the pooled variance and then the t value. The calculation based on the provided data results in a t value of approximately -3.79, indicating a significant difference between the two diets in terms of weight gain at the 0.05 significance level.

A Researcher Believes a New Diet Should Improve Weight Gain α\alphaα

A Researcher Believes a New Diet Should Improve Weight Gain $\alpha$