1. When dividing a population into subgroups so that a random sample from each subgroup can be collected, what type of sampling is used?

A. Simple random sampling

B. Systematic sampling

C. Stratified random sampling

D. Cluster sampling

2. What does the special rule of addition state?

A. P(A or B) = P(A) + P(B)

B. P(A and B) = P(A) + P(B)

C. P(A or B) = P(A) – P(B)

D. P(A and/or B) = P(A) + P(B)

3. What does the following statement equal?

A. 640

B. 36

C. 10

D. 120

4. What is the difference between a sample mean and the population mean?

A. Standard error of the mean

B. Sampling error

C. Interval estimate

D. Point estimate

5. All possible samples of size n are selected from the population and the mean of each sample is determined. The mean of the sample means will be?

A. The same as the population mean

B. Larger than the population mean

C. Smaller than the population mean

D. Cannot be estimated in advance

6. When a confidence interval for a population mean is constructed from sample data, we can conclude:

A. The population mean is in the interval

B. The population mean is not in the interval

C. For an infinite number of samples and corresponding confidence intervals, the population mean is in a stated percentage of the intervals

D. Nothing, we cannot make any inferences.

7. The t distribution is similar to the z distribution in all BUT one of the following characteristics. Which one is it?

A. Continuous

B. Symmetrical

C. Bell-shaped

D. Mean = 0 and Standard Deviation = 1

8. In hypothesis testing, what is the level of significance?

A. The risk of rejecting the null hypothesis when it is true

B. A value between 0 and 1

C. Selected before a decision rule can be formulated

D. All of the above

9. If the alternate hypothesis states that µ does not equal 4,000, where is the rejection region for the hypothesis test located?

A. Center

B. Both tails

C. Lower or left tail

D. Upper or right tail

10. If the alternative hypothesis states that µ > 6,700, where is the rejection region for the hypothesis test located?

A. Right or upper tail

B. Both tails

C. Left or lower tail

D. Centre

**Question 1 **– Galway Bay Restaurants (GBR) have several restaurants around the country Since the outbreak of COVID-19 and subsequent reduction in restaurant business, the owners of GBR are seeking to reduce wages in a bid to make some cost savings and avoid job loss. To help them inform the decision the owners of GBR would like to gain information of the amount of tip a waiter/waitress can expect of earn per bill. Analysis of 500 recent bills indicated that the waiter/waitress earned the following amounts in tips per 8- hour shift.

Amount of Tip | Number |

€0 up to €20 | 200 |

€20 up to €50 | 100 |

€50 up to €100 | 75 |

€100 up to €200 | 75 |

€200 or more | 50 |

Total | 500 |

- What is the probability of a tip of €200 or more? 10%
- Are the categories €0 up to €20, €20 up to €50, and so on considered mutually exclusive? No
- What is the probability of a tip of up to €50?
- What is the probability of a tip of less than €200?

**Question 2 –** The monthly expenditure by households on electricity bills follows a normal probability distribution with a mean of €50 and a standard deviation of €4. On the basis of this information:

- What is the probability of selecting a household whose bill is between €44 and €55?
- What is the probability of selecting a household whose bill is greater than €55?
- Compute the probability of a value between €52 and €55.

**Question 3 –** The amount of water in a 12-ounce bottle is uniformly distributed between 11.96 ounces and 12.05 ounces

- What is the mean amount per bottle
- What is the standard deviation amount per bottle?
- What is the probability of selection a bottle of water and finding it has less than 12 ounces?
- What is the probability if selecting a bottle of water and finding it has more than 11.98 ounces?

**Question 4** – The quality control department in a local medical device company employs five quality assurance technicians during the day shift. Listed below is the number of times each technician instructed the production team to shut down manufacturing last week

Technician | Shutdowns |

O’Shea | 4 |

Reilly | 3 |

Shannon | 5 |

Kenny | 3 |

O’Leary | 2 |

- How many different samples of two technicians are possible from this population
- List all possible samples of two observations each and compute the mean of each sample
- Compare the mean of the sample means with the population mean
- Compare the shape of the population distribution with the shape of the distribution of the sample means

**Question 5** – A recent study revealed that a typical NUIG student coffee drinkers consume an average of 3.1 cups per day. A sample of 12 lecturers revealed that they consumed the following amounts of coffee, reported in cups, yesterday.

3.1 3.3 3.5 2.6 2.6 4.3 4.4 3.8 3.1 4.1 3.1 3.2 |

At the 0.05 significance level, do theses sample data suggest there is a difference between student coffee drinkers sand the sample mean from the lecturers?

**Question 6** – Given the following hypothesis

HO: μ_National student lecture attendance – μ_NUIG student lecture attendance =100

H1: μ_National student lecture attendance – μ_NUIG student lecture attendance ≠ 100

A random sample of six students resulted in the following values for annual lecture attendance: 118, 105, 112, 119, 105 and 111. Assume a normal population. Using the 0.05 signifiance level can we conclude that the mean is different from 100?

- State the decision rule
- Compute the value of the t statistic
- What is your decision regarding the null hypothesis?
- Estimate the p-value