Topic 3 - Organizing and Graphing Data

1.The following data represent the total number of 20 defective cordless iron in a particular

production day.

2 3 5 7 8

9 10 13 13 15

15 15 18 19 19

20 23 26 28 29

i. Construct a frequency distribution.

ii. Using the result from part (i), calculate the relative frequencies for each class.

iii. Using the result from part (i), calculate the cumulative frequencies for each class.

iv. Construct a frequency histogram for these data (use the given graph paper).

v. Construct a frequency polygon for these data (use the given graph paper).

vi. Construct a cumulative frequency graph for these data (use the given graph paper).

2.The grocery expenses for six families were $65.48, $65.46, $80.86, $43.9, $88.75, and $81.49.

Compute the a) mean, median and mode and b) variance and standard deviation for the grocery

bill. Round to the nearest cent.

3) The first two columns of the accompanying table provide a frequency distribution, for the days to maturity of a sample of 40

short-term investments. Calculate the sample standard deviation.

Days to maturity Frequency (f)

30-39 1

40-49 6

50-59 6

60-69 9

70-79 6

Topic 5 - Hypothesis testing - single mean and proportion

1)A telephone company claims that the mean duration of all long-distance phone calls made by its

residential customers is 10 minutes. A random sample of 100 long-distance calls made by its

residential customers taken from the records of this company showed that the mean duration of calls

for this sample is 9.20 minutes. The population standard deviation is known to be 3.80 minutes. Use

2% significance level to test that the mean duration of all long-distance calls made by residential

customers is different from 10 minutes. Answer the following questions.

i. Identify the claim and state the H0 and H1.

ii .Find the critical value.

iii .Calculate the test statistic.

iv. Calculate the p-value.

v. Make a decision to reject or fail to reject the H0.

vi. Interpret the decision in the context of the original claim.

2)A soft-drink manufacturer claims that its 12-ounce cans do not contain, on average, more than 30

calories. A random sample of 64 cans of this soft drink, which were checked for calories, contained a

mean of 32 calories with a standard deviation of 3 calories. Assume that the distribution of the calories

of the soft drink is normally distributed. Use 5% significance level to determine that the mean calories

in the soft drink is not more than 30 calories. Answer the following questions.

i. Identify the claim and state the H0 and H1.

ii. Find the critical value.

iii. Calculate the test statistic.

iv. Make a decision to reject or fail to reject the H0

v. Interpret the decision in the context of the original claim

3)According to a 2018 survey by a research group, 30% of adults typically run the water for a period of 6

to 10 minutes while taking the shower). Suppose that in a recent survey of 400 adults, 104 stated that

they typically run the water for a period of 6 to 10 minutes when they take a shower. At the 5%

significance level, can you conclude that the proportion of all adults run the water for a period of 6 to

10 minutes when they take a shower is less than 0.30? Answer the following questions.

i. Identify the claim and state the H0 and H1.

ii. Find the critical value.

iii. Calculate the test statistic.

iv. Make a decision to reject or fail to reject the H0.

v. Interpret the decision in the context of the original claim.

Topic 6- Hypothesis testing - comparing two means and proportion

1)A local college cafeteria has a self-service soft ice cream machine. The cafeteria provides bowls that

can hold up to 16 ounces of ice cream. The food service manager is interested in comparing the mean

amount of ice cream dispensed by male students to the mean amount dispensed by female students.

A measurement device was placed on the ice cream machine to determine the amounts dispensed.

Random samples of 85 male and 78 female students who got ice cream were selected. The sample

means were 7.23 and 6.49 ounces for the male and female students, respectively. Assume that the

population standard deviations are 1.22 and 1.17 ounces, respectively. Use 1% significance level to

determine that the average amount of ice cream dispensed by male college students is larger than the

average amount dispensed by female college students.

Answer the following questions.

Male student. Female student

Mean sample 7.23 oz 6.49 oz

Population standard deviation. 1.22 oz 1.17 oz

Sample size 85 78

i. Identify the claim and state the H0 and H1.

ii. Find the critical value.

iii. Calculate the test statistic.

iv. Make a decision to reject or fail to reject the H0.

v.Interpret the decision in the context of the original claim.

2)An insurance company wants to know if the average speed at which men drive cars is greater than

that of women drivers. The company took a random sample of 27 cars driven by men on a highway

and found the mean speed to be 72 miles per hour with a standard deviation of 2.2 miles per hour.

Another sample of 18 cars driven by women on the same highway gave a mean speed of 68 miles per

hour with a standard deviation of 2.5 miles per hour. Assume that the speeds at which all men and all

women drive cars on this highway are both normally distributed with equal standard deviation. Use 1%

significance level to test the hypothesis that the mean speed of cars driven by all men drivers on this

highway is greater than that of cars driven by all women driver.

Answer the following questions.

Man driver Women driver

Mean sample 72 mph 68 mph

Sample standard deviation 2.2 mph 2.5 mph

Sample size 27 18

i. Identify the claim and state the H0 and H1.

ii. .Find the critical value.

iii .Calculate the test statistic.

iv .Make a decision to reject or fail to reject the H0.

v. Interpret the decision in the context of the original claim.

3)The manufacturer of a gasoline additive claims that the use of this additive increases gasoline

mileage. A random sample of six cars was selected, and these cars were driven for 1 week without the

gasoline additive and then for 1 week with the gasoline additive. The following table gives the miles

per gallon for these cars without and with the gasoline additive. Use 2.5% significance level to

determine that the use of gasoline additive increases the gasoline mileage.

Answer the following questions.

Cars 1 2 3 4 5 6

Miles Without additive 24.6 28.3 18.9 23.7 15.4 29.5

per gallon With additive 26.3 31.7 18.2 25.3 18.3 30.9

i. Identify the claim and state the H0 and H1.

ii. Find the critical value.

iii. Calculate the test statistic.

iv .Make a decision to reject or fail to reject the H0.

v. Interpret the decision in the context of the orignal claim.