4. A questionnaire asks the respondents to write their responses in about 100 words. To test if the mean number of words in the responses is 100 words or it is different from 100 words, a simple random sample of 12 responses will be taken. a) State the null hypothesis and the alternative hypothesis. H : u = 100 H : H # 100 b) The following are the word counts from a simple random sample of 12 responses. word counts 95 101 102 106 106 106 108 109 111 112 115 117 With a boxplot of this data 95 96 98 100 102 104 106 108 110 112 114 116 117 Does the boxplot show any heavy outliers? Why do we have to examine this point? c) State whether you would accept or reject the null hypothesis at 1% level of significance. d) Construct a 99% confidence interval for the mean of the number of words in all the responses. e) Does your 99% confidence interval contain the value 100? No f) Write about relationship between a two sided hypothesis test and a related confidence interval