Statistics and Probability Answers

The mean length of certain construction lumber is supposed to be 8.5 feet. A random

sample of 21 pieces of such lumbers gives a sample mean of 8.3 feet and a sample

standard deviation of 1.2 feet. A builder claims that the mean of the lumber is different

from 8.5 feet. Does the datasupport the builder's claim at a= 0.05?

Step:

1.State the null and alternative hypothesis concerning the population mean, "\\mu" and the type of test to be used.

2.Specify the level of significance "\\alpha"

3.State the decision rule

4.Collect the data and perform calculations.

5. Make a statistical decision.

6.State the conclusion.

A supermarket boasts that checkout times for customers are never more than 15 minutes. A random sample of 36 costumers reveals a mean checkout time of 17 minutes with a standard deviation of 3 minutes. What can you conclude about the supermarket’s boast at the 0.05 level? 

A coin is tossed 10 times. Find the probability that at least three are tails.

A population consists of the four number (2,3,6,9).

Consider all possible samples of size 2 that can be drawn with replacement from this population. Answer the following:

a. List all possible samples of size 2 which can be drawn with replacement from this population.

b. Compute the Population mean.

c. Compute the Population Standard deviation.

d. Find the mean of the sampling distribution.

DIRECTIONS: In each problem below, give the null and alternative hypothesis and

identify whether it is right-tailed, left-tailed or two-tailed test.

3. A quality control engineer is testing the battery life of a new smartphone. The company

is advertising that the battery lasts 24 hours on full- charge, but the engineer suspects that the

battery life is actually less than that. They take a random sample of 50 of these if their average

battery life is significantly less than 34 hours.

4. In the past, the mean running time for a certain type of radio battery has been 9.6 hours.

The manufacturer has introduced a change in then production method and wants to perform a

hypothesis test to determine whether the mean running time has changed as a result.

5. In a random sample of 400 electronic gadgets, 14 were found to be defective. The

manufacturer wants to claim that more than 5% of all the gadgets are defective. Test this claim at

the 0.01 level of significance.

DIRECTIONS: In each problem below, give the null and alternative hypothesis and

identify whether it is right-tailed, left-tailed or two-tailed test.

1. A newspaper report claims that 30% of all tea-drinkers prefer green tea to black tea.

Leo is office manager at a company with thousands of employees. He wonders if the

newspaper's claim holds true at his company. To find out, Leo asks a simple random sample of

125 tea-drinking employees which they prefer: green tea or black tea.

2. A city had an employment rate of 70%. The mayor pledge to lower this figure and

supported programs to decrease unemployment. A group of citizens wanted to test if the

unemployment rate had actually decreased, so they obtained a random sample of citizens to see

what proportion of the sample was unemployed.

The average amount of rainfall during the summer months is 11.52 inches. A researcher in

PAGASA selects a random sample of 10 provinces and finds that the average amount of

rainfalllast year was 7.42 inches with a standard deviation of 1.3 inches. At 0.01 level

significance, can it be concluded that the mean rainfall last year was below 11.52 inches?

Step

1. State the null and alterative hypothesis

concerning the population mean, "\\mu" and the type of test to be used.

2. Specify the level of significance "\\alpha"

3.State the decision rule.

4. Collect the data and perform calculations.

5.Make a statistical decision.

6. State the conclusion.

The amount of time devoted to preparing for a statistics examination by students is a normally distributed random variable with a mean of 17 hours and a standard deviation of 5 hours.

Required:

a) What is the amount of time below which only 15% of all students spend studying?

b) What is the amount of time above which only one third of all students spend studying? c) What is the probability that a student spends between 16 and 20 hours studying?

d) What is the probability that a student spends at least 15 hours studying?

e) What is the probability that a student spends at most 18 hours studying?