# solve the problem please show step by step solutions Q 1)A variable of two populations has a mean of 8.9 and a standard deviation of 3 for one of the populations and a mean of 9.3 and a standard...

**solve the problem please show step by step solutions**

**Q 1)A variable of two populations has a mean of 8.9 and a standard deviation**

**of 3 for one of the populations and a mean of 9.3 and a standard**

**deviation of 3.8 for the other population. For independent samples of**

**sizes 4 and 5, respectively, find the mean of x1 - x2.**

**Q 2 )Preliminary data analyses indicates that use of a paired t** **-test is reasonable. Perform the hypothesis test ****solve the problem please show step by step solutions**

**by using either the critical****-****value approach or the P****-****value approach as indicated. Assume that the null**

**hypothesis is H0 : ?1** **=** **?2.**

**The table below shows the weights, in pounds, of seven subjects before**

**and after following a particular diet for two months.**

**Subject A B C D E F G**

**Before 164 199 196 191 193 184 168**

**After 157 190 194 196 179 186 156**

**At the 1% significance level, do the data provide sufficient evidence to**

**conclude that the diet is effective in reducing weight? Use the P-value**

**approach.**

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### 2 Answers

A variable of two populations has a mean of 8.9 and a standard deviation of 3 for one of the populations and a mean of 9.3 and a standard deviation of 3.8 for the other population. Independent samples of sizes 4 and 5, respectively are taken from the two populations. The mean of the two samples has to be determined.

The mean of the two samples is equal to `(8.9*4 + 9.3*5)/9 = 9.12` . The standard deviation is `sqrt(4*3^2 + 5*3.8^2) = 10.4`

**Sources:**

Answer of question 1:

Combined mean of 2 samples = (n1x1+n2x2)/n1+n2

n1 = 4, x1 = 8.9;

n2 = 5,x2 = 9.3

Combined mean =( (4×8.9)+(5×9.3))/4+5

= 9.12