A clinical psychologist wanted to examine the relative effectiveness of cognitive-behavioral therapy (CBT) and behavioral therapy (BT) for depression. A sample of 20 depression patients were randomly selected and assigned to either of the two therapy methods. The data below presents the effectiveness rated by independent judges. Test whether one method is better than the other at .05 significance level (non-directional) by answering the following questions? CBT: 4, 8, 5, 7, 6, 9, 8, 6, 7, 8 BT: 3, 5, 4, 8, 6, 2, 4, 6, 5, 7

Noise pollution is measured in decibels. In California any motorcycle made after 1980 may not be any louder than 80 decibels.  Harley Davidson claims their mean decibel rating on bikes is 70 with a variance of 10.  The variance of the noise is questioned.  Just because Harley has a mean that is less than 80, they could still be producing louder than acceptable bikes.  The federal EPA conducts a sample of 30 bikes and determines the variance to be 20 decibels.  Is there enough evidence to question Harley’s claim of 10 decibels?

Earlier this semester, we learned to use 2-Sample-TTest to compare the population means of two independent populations. One-way ANOVA is more powerful because it could compare the population means of three or more independent populations. However, use of one-way ANOVA also requires the assumption that the populations have the same variance. In this exercise, we will compare and contrast One-way ANOVA and 2-Sample-TTest. With the 2-Sample- TTEST, we will first choose 'No' for the pooled variances option, then re-run the test while choosing 'Yes' for the pooled variances option. Use the following data to complete these tasks. Depending on if you choose to do this by hand or using code, use the data format that suits you best - LONG form on top or WIDE form on bottom. Treatment One One One One One One One Two Two Two Two Two Two Two Treatment One 7.1 8.5 7.6 7.7 6.9 8.5 7.8 Response 7.1 8.5 7.6 7.7 6.9 8.5 7.8 1.4 4.1 4.3 3.9 4 4 4.6 p-value= Treatment Two 1.4 4.1 4.3 3.9 4 4 4.6 1. Use…

Records from previous years for a casualty insurance company show that its clients average a combined total of 1.9 auto accidents per day, with a variance of 0.31. The actuaries of the company claim that the current variance, oʻ, of the number of accidents per day is not equal to 0.31. A random sample of 17 recent days had a mean of 2 accidents per day with a variance of 0.62. If we assume that the number of accidents per day is approximately normally distributed, is there sufficient evidence to conclude, at the 0.05 level of significance, that the actuaries are correct? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H,. p H, :0 H, :0 (b) Determine the type of test statistic to use. (Choose one) ▼ D=0 OSO O20 (c) Find the value of the test statistic. (Round…