The researcher also wanted to estimate the proportion of NZ "data businesses" that had a removed register status and the proportion of NZ "science businesses" that had a removed register status. They found that 95 of the 150 NZ "data businesses" had a removed register status and 75 of the 150 NZ "science businesses" had a removed register status. If the researcher constructed VIT bootstrap confidence intervals for the proportion of businesses with a removed register status (one for "data businesses" and one for "science businesses"), the confidence interval based on the sample of NZ "data businesses" will be

3 Use the information below to answer the questions in this section. Recall that in Section 1, a researcher obtained a random sample of 150 "data businesses" and 150 "science businesses" from the NZB (New Zealand Business Number) registry. For each of the businesses in both samples that were currently registered (i.e., not removed, in liquidation or inactive), the researcher looked up the date of the registration and recorded how many years since the business had been registered. For example, if the business was registered in 2023, the value for years_since_registered was recorded as 0, and if the business was registered in 2020, the value for years_since_registered was recorded as 3. A researcher was interested in confirming that, for all currently registered businesses, the mean years since a "data business" was registered is either higher or lower than the mean vears since a "science business" was registered. They decided to carry out a two-sample t-test using iNZight Lite. Below is part of the output produced 3(a) Which of the following is a suitable two-sided alternative hypothesis for this test? Select one alternative • The underlying mean years since a "data business" was registered is the same as the underlying mean years since a "science business" was registered O The undertying mean years since a data bu signs 'as registered is not the same as • The underlying mean years since a "data business" was registered is higher than the underlying mean years since a "science business" was registered

2(c) To compare the proportion of Mäori authorities that have a social media presence with the proportion of other Maori enterprises that have a social media presence, a 95% confidence interval was constructed for the difference of two proportions using the order Maori authorities - other Maori enterprises. The limits of this confidence interval are (-0.141, -0.079). Based on this confidence interval, we (can? cannot>??claim that the proportion of all Mäori authorities that have a social media presence is lower than the proportion of all other Maori enterprises that have a social media presence.

Then use the confidence interval (-0.004, 0.104) calculated for this sampling situation chosen by this student to answer the following research question: How does the proportion of all Maori authorities who use social media to gather feedback or resolve customer concerns compare to the proportion of all Maori authorities who use social media to monitor social media activity of other businesses or customers?

In a random sample of 373 people that were tested for the Norcovirus, it was found that 321 did not have the virus. A 94% confidence interval was constructed to estimate the proportion of the population that does not have the Norcovirus. This confidence interval came out to be (0.83,0.89).Select the correct intrepretation of this interval.We are 94% confident that the proportion of people in the sample that tested postitive for the Norcovirus is between 83% and 89%.We are 94% confident that the proportion of people in the sample that tested negative for the Norcovirus is between 83% and 89%.We are 94% confident that the proportion of the population that have the Norcovirus is between 83% and 89%.We are 94% confident that the proportion of the population that does not have the Norcovirus is between 83% and 89%.

Use the bootstrap distribution for a sample proportion above to estimate a 95% confidence interval. Give your answers to 2 decimal places (2dp).Lower Limit: Answer 1 Question 16 Upper Limit: Answer 2 Question 16Give the symbol for the parameter being estimated in this case: Answer 3 Question 16