For a random sample of 36 data pairs, the sample mean of the differences was 0.77. The sample standard deviation of the differences was 2. At the 5% level of significance, test the claim that the population mean of the differences is different from 0.
Extracted text: (a) Is it appropriate to use a Student's t distribution for the sample test statistic? Explain. O Yes, the sample size is larger than 30. O No, the standard deviation is not smaller than the sample mean. O Yes, the standard deviation is larger than the sample mean. O No, the sample size is not larger than 30. What degrees of freedom are used? (b) State the hypotheses. O Ho: Ha = 0; H,: H# 0 O Ho: Hd = 0; H1: Hd>0 O Ho: Hd = 0; H4: Hd <0 o="" ho:="" hg#="" 0;="" hq:="" hd="0" (c)="" compute="" the="" t="" value.="" (round="" your="" answer="" to="" three="" decimal="" places.)="" (d)="" estimate="" the="" p-value="" of="" the="" sample="" test="" statistic.="" o="" p-value=""> 0.500 O 0.250 < p-value="">< 0.500="" o="" 0.100="">< p-value="">< 0.250="" o="" 0.050="">< p-value="">< 0.100="" o="" 0.010="">< p-value="">< 0.050="" o="" p-value="">< 0.010 (e) do we reject or fail to reject the null hypothesis? explain. o at the a = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. o at the a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. o at the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. o at the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (f) what do your results tell you? o fail to reject the null hypothesis, there is sufficient evidence to conclude that the population mean of the differences is not zero. o reject the null hypothesis, there is sufficient evidence to conclude that the population mean of the differences is not zero. o fail to reject the null hypothesis, there is insufficient evidence to conclude that the population mean of the differences is not zero. o reject the null hypothesis, there is insufficient evidence to conclude that the population mean of the differences is not zero. 0.010="" (e)="" do="" we="" reject="" or="" fail="" to="" reject="" the="" null="" hypothesis?="" explain.="" o="" at="" the="" a="0.05" level,="" we="" reject="" the="" null="" hypothesis="" and="" conclude="" the="" data="" are="" not="" statistically="" significant.="" o="" at="" the="" a="0.05" level,="" we="" reject="" the="" null="" hypothesis="" and="" conclude="" the="" data="" are="" statistically="" significant.="" o="" at="" the="" a="0.05" level,="" we="" fail="" to="" reject="" the="" null="" hypothesis="" and="" conclude="" the="" data="" are="" statistically="" significant.="" o="" at="" the="" a="0.05" level,="" we="" fail="" to="" reject="" the="" null="" hypothesis="" and="" conclude="" the="" data="" are="" not="" statistically="" significant.="" (f)="" what="" do="" your="" results="" tell="" you?="" o="" fail="" to="" reject="" the="" null="" hypothesis,="" there="" is="" sufficient="" evidence="" to="" conclude="" that="" the="" population="" mean="" of="" the="" differences="" is="" not="" zero.="" o="" reject="" the="" null="" hypothesis,="" there="" is="" sufficient="" evidence="" to="" conclude="" that="" the="" population="" mean="" of="" the="" differences="" is="" not="" zero.="" o="" fail="" to="" reject="" the="" null="" hypothesis,="" there="" is="" insufficient="" evidence="" to="" conclude="" that="" the="" population="" mean="" of="" the="" differences="" is="" not="" zero.="" o="" reject="" the="" null="" hypothesis,="" there="" is="" insufficient="" evidence="" to="" conclude="" that="" the="" population="" mean="" of="" the="" differences="" is="" not="">