Please only do question 3. Show step by step and with explanation (if needed). T

Question

Please only do question 3. Show step by step and with explanation (if needed). Thanks :)

2. A recent study examined the effects of peoples pub spending habits both before and after getting a pay raise. Consider the following randomly collected data. before I after 32 43 33 36 36 31 31 30 32 28 29 36 28 27 39 36 26 36 300 32 32 32 300 36 Test at 90% confidence if peoples pub spending habits increase after getting a pay raise if we assume the population variances are not the same. Up to what confidence could we say make the claim that is does increase?

Explanation / Answer

3. From the same person. so varance will be same.

we will do , paired t test.

the test statistic of paired t test is :

calculation

here the value of the test statistic is  t = -1.2796

and p value under null hypothesis is :p-value = 0.2148

90% confidence interval

90 percent confidence interval:
-4.8861873 0.7195206

so, we conclude :  true difference in means is equal to 0

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