Statistics and Probability Answers

 Determine the direction of the hypothesis test (one-sided left, one-sided right, bidirectional)
 Determine the test statistic (z* or t*) and the p-value for each of the following situations and
 Determine if they would cause the rejection of the null hypothesis if the confidence level was set
at 95% in each case. (Hint: be wary of the sample size) [2 points each]:
a) Ho: μ = 50 mL, Ha: μ ≠ 50 mL, sample mean = 48.1 mL, sample standard deviation = 5, n = 40
b) Ho: μ ≤ 8.4 m3, Ha: μ > 8.4 m3, sample mean = 10 m3, s = 3.5, n = 25
c) Ho: μ ≥ 20oC, Ha: μ < 20oC , sample mean = 17.1oC, s =4.6oC, n = 12
d) Ho: μ = 357 s, Ha: μ ≠ 380 s, sample mean = 410 s, s = 75, n = 40
e) Ho: μ ≤ 46 units, Ha: μ > 46 units, sample mean = 50 units, s = 9.5, n = 41

The Department of Foreign Languages of a liberal arts college conducted a survey of its recent graduates to determine the foreign language courses they had taken while undergraduates at the college. Of the 530 graduates
209 had at least one year of Spanish.
176 had at least one year of French.
142 had at least one year of German.
47 had at least one year of Spanish and French.
31 had at least one year of Spanish and German.
27 had at least one year of French and German.
7 had at least one year of all three languages.
(a) How many of the graduates had at least 1 yr of at least one of the three languages?
(b) How many of the graduates had at least 1 yr of exactly one of the three languages?
(c) How many of the graduates had less than 1 yr of any of the three languages?

From the list of populations and samples, which samples are representative of the population?

-Population: Healthy adults from single geographical area for a vaccine study. Sample: Employees at a local factory

-Population: Individuals infected with hepatitis C virus. Sample: Patients presenting with hepatitis C virus at a liver clinic in a teaching hospital

-Population: Women diagnosed with breast cancer between 1990 and 1999. Sample: Women first attending hospital with breast cancer between 1990 and 1999

-Pop: study of the general population to assess the prevalence of a number of blood-borne viruses. Sample: Blood donors

Based on studies conducted in various regions across the country, the average cost of pumpkins for consumers is $3.18 per kg.
From a random sample of 15 farmer’s markets in the Montreal-area you determine that the average price for pumpkins is $4.25 per kg with a standard deviation of $1.90 per kg.
d) Construct a 98% confidence interval for the average price of pumpkins in the Montreal-area if the statistics remained unchanged despite the fact that 20 more markets were sampled and determine if it differs significantly from that of the rest of the country.
e) Construct a 95% confidence interval for the average price of pumpkins in the Montreal-area if a new sample of 15 pumpkins yields a sample mean of $4.52 per kg. and a standard deviation of $2.50 per kg. Determine if it differs significantly from that of the rest of the country.
f) Give two reasons that explain the difference in the length of the confidence interval you calculated in part c and in part d.

Based on studies conducted in various regions across the country, the average cost of pumpkins for consumers is $3.18 per kg.
From a random sample of 15 farmer’s markets in the Montreal-area you determine that the average price for pumpkins is $4.25 per kg with a standard deviation of $1.90 per kg.
a) Determine the minimum sample size necessary to construct a 95% confidence interval with maximal error of E = 0.5 for the mean price of pumpkins
b) Construct a 95% confidence interval for the average price of pumpkins in the Montreal-area and determine if it differs significantly from that of the rest of the country.

The organizer of the Montreal International Art Exhibit is trying to determine its optimal operating hours for its next one-day exhibition. Studies have shown that the arrival times at any given exhibition form a normal distribution with the average time that visitors arrive being 2 hours and 56 minutes after doors open, with a standard deviation of 48 minutes.

a) If the organizer sets the opening of the exhibition at 10:00 a.m., at what time would they expect 95% of the visitors to have arrived?
b) If the organizer sets the opening of the exhibition at 9:00 a.m., at what time after the doors open will only 15% of the visitors have arrived?
c) At what time should the organizer open the exhibition if they would like 70% of the visitors to have arrived by 1:00 p.m. so that they can award the first door prize?

Pick the following types of figures that would be appropriate for illustrating the relationship between gender and blood group in a sample of adults.

*Note there can be either one or multiple correct answers*

A. Bar chart

B. Pie chart

C. Stem-and-leaf plot

D. Histogram

E. Box-plot

F. Clustered bar chart

G. Segmented bar chart

H. Scatterplot

From the list of populations and samples, select all of the samples that are likely to be representative (not biased) of the population from which they are drawn.

*there can be only 1 or multiple correct possible answers*

A. Population: Healthy adults from a single geographical area for a vaccine study. Sample: Employees at a local factory

B. Population: Individuals infected with hepatitis C virus. Sample: Patients presenting with hepatitis C virus at a liver clinic in a teaching hospital

C. Population: Women diagnosed with breast cancer between 1990 and 1999. Sample: Women first attending hospital with breast cancer between 1990 and 1999

D. Population: A study of the general population to assess the prevalence of a number of blood-borne viruses. Sample: Blood donors

Crispy Chips is a potato chip company that is quite popular for its low-fat, low-calorie bags of potato chips. The procedure used at its production plant allows for 65 chips to be inserted into each bag for distribution to consumers. However, given that chip-making is not an exact science, there is a standard deviation of 5 chips per individual bag. If we can assume that the amount of chips in each bag forms a normal distribution, calculate the following:

Q. Define the following terms
(i) Geometric distribution
(ii) Binomial distribution
(ii) Continuous bivariate distribution