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

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

1(a) A research question that asks - What is the mean number of characters used in the names of NZ "data businesses" in the researcher's sample? - would require a sample-to-population inference

The researcher then carried out a similar sampling and inference approach but focused on comparing "human businesses" (businesses with the word "human" in their name and "psychology businesses" (businesses with the word "psychology" in their name). Compare the two different statements shown below, in terms of the strength of evidence and the provided confidence interval. One of these statements is incorrect and one is correct .Statement A There is some evidence that for all currently registered businesses, the mean years since a "human business* was registered is higher than the mean years since a "psychology business" was registered. Difference in group means with 95% Confidence human- psychology Estimate 3.135 Lower 0.439 Upper 5.832 Statement B There is strong evidence that for all currently registered businesses, the mean years since a "human business* was registered is higher than the mean years since a "psychology business" was registered. Difference in group means with 95% Confidence human- psychology Estimate 1.135 Lower -1.561 Upper 3.832 Clearly identify which one of the two statements is incorrect, by stating Statement A or Statement B. explain no more than two sentences

The NZBN register is available on the website nzb. govt.nz and provides a search tool to look up key information about New Zealand businesses, including • their NZBN. • official business name, • register status (registered, in liquidation, inactive, removed). • the year the business was registered To access information about a business requires first searching for a business using words in their name (or a specific NZBN), then clicking the link for each business given in the search results to open up a separate page about that business A researcher searched for businesses with the word "data" in their name, and the website returned a total of 2088 different businesses. The researcher then took a random sample of 150 of these "data businesses" to analyse. Similarly, the researcher searched for businesses with the word "science" in their name, and the website returned a total of 848 different businesses. After removing businesses that also had the word data in their name, the researcher then took a random sample of 150 of these "science businesses" to analyse The researcher wanted to estimate the mean number of characters used in the names of NZ data businesses" and the mean number of characters used in the names of NZ "science businesses" They created the variable num_chars_business_name by using the function =/en) within Google Sheets to count the number of characters used in each business name. The researcher then produced the plots below as part of their investigation.

Long-established firms with successful track records probably have accumulated much ______.Multiple choice question.business know-howphysical capital