**Question 1.**

**The following set of data is the mark (out of 100) for 30 students in a final exam.**

82 51 78 93 33 41 35 40 29 84 51 82 88 47 85

44 85 80 49 78 91 71 38 77 54 75 45 83 32 37

**(a) ** Use SPSS commands: Explore to:

**(i) **Generate descriptive statistics. [See pages 9-13, SPSS Tutorial, available on Cecil.]

**(ii)** Create a stem-and-leaf plot of the data.

**(iii) **Create a box plot of the data.

**(b) **Briefly comment on what the plots reveal.

**Question 2.**

A store manager was interested in the number of items purchased by customers in each transaction. He took a sample of 100 transactions and recorded the number of items purchased in each one. The resulting data is given in the following frequency table:

Number of items | Frequency |

1 | 7 |

2 | 23 |

3 | 29 |

4 | 19 |

5 | 8 |

6 | 14 |

Toatl | 100 |

What are the sample mean and sample standard deviation of these 100 observations?

[Note: Show the sample standard deviation to 3 decimal places.]

**Question 3.**

In 2008, Statistics New Zealand began collecting data on the working life of New Zealanders. They surveyed more than 14,500 people in March 2008. The following table shows the usual number of hours worked per week, broken down by type of worker.

**Use the table above to estimate the following:**

**(a) **What proportion of workers usually worked between 30 and 49 hours per week?

**(b) **Of workers who usually worked 40 hours per week, what proportion were self-employed?

**(c) **What proportion of self-employed workers usually worked 40 hours per week?

**(d) ** Given that a randomly selected worker is self-employed, what is the probability they usually worked 40 hours per week?

**(e) **What is the probability that a randomly chosen worker is self-employed and usually worked 40 hours per week?

**(f) **Which category of worker had the highest proportion of workers that usually worked at least 60 hours per week?

**Question 4. **

The National Survey of Adolescent Health interviewed 4877 teenage Americans. One question asked was “What do you think are the chances you will be married in the next 10 years?”. Of the 2625 females teenagers who answered the survey, 716 answered “at most 50%”, while 1466 male teenagers answered “more than 50%”.

**Use this information to answer the following:**

**(a) **Construct a 2 x 2 table of counts displaying the results for this study. Complete the table.

**(b) **(i) Given that a randomly selected teenager is female, what is the probability they think they have more than a 50% chance of being married in the next 10 years?

**(ii) **Given that a randomly selected teenager is male, what is the probability they think they have more than a 50% chance of being married in the next 10 years?

**(iii) **How many times more likely is a randomly selected female teenager to think they have more than a 50% chance of being married in the next 10 years than a male teenager?

**Question 5.**

A statistics student was interested in investigating how long it takes to get a pizza delivered from the local pizzeria. Over a few weeks, a random sample of 10 delivery times (in minutes) was recorded. The data are displayed below:

23.4, 19.2, 28.4, 21.3, 17.9, 22.2, 29.3, 33.1, 13.6, 18.3

**(a) ** What are the sample mean and sample standard deviation of these 10 observations?

**(b) ** Calculate a 95% confidence interval for the mean delivery time. Interpret your results.

**Question 6.**

Southern Cross Travel Insurance commissioned a survey about New Zealander’s travel in late 2014. Some of the results are shown below:

**(a) **State the sampling situation (a, b or c) for calculating the standard error of the difference in the following scenarios:

**(i) **for people who had traveled overseas, estimating the difference between the proportion of people under 40 who thought creepy crawlies were the biggest irritant while traveling and the proportion of people 40 or over who thought creepy crawlies were the biggest irritant while traveling.

**(ii)** For people who had traveled overseas, estimating the difference between the proportion of people under 40 who thought creepy crawlies were the biggest irritant while traveling and the proportion of people under 40 who thought delays were the biggest irritant while traveling.

**(iii)** For people who researched countries, estimating the difference between the proportion of females who researched shopping/food and the proportion of males who researched shopping/food.

**(b) **For people who researched countries, calculate a 95% confidence interval for the difference between the proportion of females who researched accommodation and the proportion of females who researched tourist attractions.

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