Search & Filtering
The human resource manager at a car dealership wants to know if the ages of its employees are
related to the department that they work in. Data was compiled and tabulated in a 2-way
contingency table. The employees were classified according to their age and department.
Expected counts are printed below observed counts
Sales Accounts Marketing Repairs Total
20-29 8 10 27 43 88
17.74 *** 26.20 23.62
30-39 29 26 38 22 *
23.18 26.72 34.24 30.86
40-49 33 32 72 82 219
44.15 50.88 65.20 58.77
50-59 81 106 86 54 327
65.92 75.97 97.36 87.75
Total 151 ** 223 201 749
Chi-Sq = 5.348 + **** + 0.024 + 15.912 +
1.459 + 0.019 + 0.413 + 2.544 +
2.816 + 7.003 + 0.709 + 9.182 +
3.448 + 11.875 + 1.325 + 12.983 = 80.395
DF = *****, P-Value = ******
No cells with expected counts less than 5.
a) Name the random variables present in the table above. [2]
b) Carefully define the null and alternative hypotheses of the Chi Square test
underlying the generation of the above table.
In 2015, the average duration of long-distance telephone calls from a certain town was 9.4 minutes. A telephone company wants to perform a test to determine whether this average duration of long-distance calls has changed. Twenty calls, originating from the town, was randomly selected and the mean duration was 10.2 minutes with standard deviation 4.8 minutes. a) Using a 1% level of significance, Complete the following: i. Give the null and alternative hypothesis of this test. [2] ii. Determine the critical value(s) of this test. [2] iii. Compute the value of the test statistic. [2] iv. State the decision rule. [1] v. Give your decision based on the available sample evidence. [1] vi. Hence, state your conclusion. [2] b) Construct the 99% confidence interval for the population mean duration of the longdistance calls from the town. [4]
During a water shortage, restaurant owners were asked not to serve water before meals, unless the customer requested water. Over a three-month period, a restaurant owner observed that 45% of the customers asked for water. After the three-month period, the owner placed a card at each table, explaining the restaurant’s policy of not serving water to customers, unless specifically asked to do so, because of the water shortage. If 53 of the next 150 customers asked for water with their meal, can we conclude that placing the cards at each table decreased the number of customers requesting water before their meal? At the 0.02 level of significance, use the following hypothesis test
A map and GPS application for a smartphone was tested for accuracy. The
experiment yielded 26 error out of the 74 trials. Find the 95% confidence interval
estimate for the proportion of errors
A study of 415 kindergarten students showed that they have seen on average
5000 hours of television. If the sample standard deviation of the population is
900, find the 95% confidence level of the mean for all students. If a parent
claimed that his children watched 4000 hours, would the claim be believable?
Phi Beta Sigma has a raffle for a trip to the mountains valued at $500. If 1000 tickets are sold at $1 each, what is the
expected value of one ticket? Write your p(x) as decimals rounded to FIVE decimal places, if needed.
Snakes shed their skin to enable growth. If the time it takes for a snake to shed its akin is normally distributed with mean of 8 days and standard deviation of 2 days, what is the probability that a snake will shed its skin after 7 days?
Suppose a random variable is normally distributed. The probabilities for 85 and 142 are 10% and 65%, respectively. Find the mean and standard deviation tp the nearest whole number.
A paint-store chain produces and sells latex and semigloss paint. Based on long-range sales, the probability that a customer will purchase latex paint is 0.75. Of those that purchase latex paint, 60% also purchase rollers. But only 30% of semigloss paint buyers purchase rollers. A randomly selected buyer purchases a roller and a can of paint. What is the probability that the paint is latex?
The lengths (in minutes) of a random selection of popular children’s animated films are listed below. Estimate the true mean length of all children’s animated films with 95% confidence.
91 85 77 94 80 90 78 100 78 76
a. Sample mean:
b. Sample standard deviation:
c. Margin of error:
d. Confidence interval: __________ < mu< __________
