Deck 10: One-Sample Tests of Hypothesis

Question 1

An alternate hypothesis is a statement about a population parameter that is accepted when the null hypothesis is rejected.

Answer 1

True

Question 2

If the null hypothesis is true and the researchers do not reject it,then a correct decision has been made.

Answer 2

True

Question 3

Type II error is the probability or risk of rejecting a null hypothesis when it is actually true.

Answer 3

False

Question 4

The researcher must decide on the level of significance before formulating a decision rule and collecting sample data.

Question 5

The region or area of rejection defines the location of all values that are so large or so small that the probability of their occurrence under a true null hypothesis is rather remote.

Question 6

For a one-tailed test using the 0.05 level of significance,the critical value for the z test is 1.645,but for t it is 1.96.

Question 7

The probability of a Type I error is also referred to as alpha.

Question 8

The level of significance is the risk of rejecting the null hypothesis when it is actually true.

Question 9

To set up a decision rule,the sampling distribution is divided into two regions - a region of non-rejection and a region where the null hypothesis is rejected.

Question 10

If the null hypothesis is and the alternate hypothesis states that µ is less than 200,then,a two-tail test is being conducted.

Question 11

As sample sizes decrease,we are more confident in sample estimates of population parameters.

Question 12

A test statistic is a value computed from sample information and used to test the null hypothesis.

Question 13

The 0.05 level of significance is applied to all studies involving sampling.

Question 14

Records on a fleet of trucks reveal that the average life of a set of spark plugs is normally distributed with a mean of 22,100 miles.A manufacturer of spark plugs claims that its plugs have an average life in excess of 22,100 miles.The fleet owner purchased 18 sets and found that the sample average life was 23,400 miles,the sample standard deviation was 1,500 miles and the computed t = 3.677.Based on these findings,there is enough evidence to accept the manufacturer's claim at the 0.05 level.

Question 15

As sample sizes decrease,the variability of sample means increases.

Question 16

A Type I error is the probability of accepting a true null hypothesis.

Question 17

If the null hypothesis is false and the researchers do not reject it,then a Type I error has been made.

Question 18

As sample sizes decrease,rejecting the null hypotheses is less likely.

Question 19

Hypothesis testing is a procedure that uses sample evidence and probability theory to decide whether to reject or fail to reject a hypothesis.

Question 20

When the population standard deviation is unknown,the test statistic used to test a hypothesis is the Student's t distribution.

Question 21

When testing a hypothesis,a test statistic is required to compute a p-value.

Question 22

For a one-tailed null hypothesis and a test statistic,Z = 1.96,the p-value is 0.025.

Question 23

To prevent bias,the level of significance is selected before setting up the decision rule and sampling the population.

Question 24

When testing a hypothesis about a proportion,the data collection is based on counting something.

Question 25

The first step in testing a hypothesis is to state the decision rule.

Question 26

The null hypothesis is rejected when a p-value is less than a stated significance level.

Question 27

If a p-value is 0.75,it is very likely that the null hypothesis is false and would be rejected.

Question 28

If the null hypothesis is false and the researcher rejects it,then a Type II error has been committed.

Question 29

A p-value is a probability.

Question 30

When the p-value is 0.001 or less,there is extremely strong evidence that the null hypothesis is true.

Question 31

If a p-value is 0.75,it is very likely that the null hypothesis is true.

Question 32

The fifth and final step in testing a hypothesis is taking a sample and,based on the decision rule,deciding if the null hypothesis should be rejected.

Question 33

A Type I error is the probability of rejecting a true null hypothesis.

Question 34

When the p-value is 0.001 or less,there is extremely strong evidence that the null hypothesis is not true.

Question 35

A p-value is the same as a stated significance level.

Question 36

Assuming that the null hypothesis is true,a p-value is the probability of observing a sample value greater than and/or less than an observed sample observation.

Question 37

If we do not reject the null hypothesis based on sample evidence,we have proven beyond doubt that the null hypothesis is true.

Question 38

The null hypothesis is rejected when a p-value is greater than a stated significance level.

Question 39

One assumption in testing a hypothesis about a proportion is that an outcome of an experiment can be classified into two mutually exclusive categories,namely,a success or a failure.

Question 40

For a one-tailed test of hypothesis,the area of rejection is only in one tail of the curve.

Question 41

If the critical values of the test statistic z are $\pm$ 1.96,they are the dividing points between the areas of rejection and non-rejection.

Question 42

What is the level of significance?

A)Probability of a Type II error
B)Probability of a Type I error
C)z-value of 1.96
D)Beta error

Question 43

If the alternate hypothesis states that µ does not equal 4,000,what is the rejection region for the hypothesis test?

A)Both tails
B)Lower or left tail
C)Upper or right tail
D)Center

Question 44

To conduct a test of proportions,the assumptions required for the binomial distribution must be met.

Question 45

A manufacturer wants to increase the shelf life of a line of cake mixes.Past records indicate that the average shelf life of the mix is 216 days.After a revised mix has been developed,a sample of nine boxes of cake mix gave these shelf lives (in days): 215,217,218,219,216,217,217,218 and 218.At the 0.025 level,has the shelf life of the cake mix increased?

A)Yes,because computed t is greater than the critical value.
B)Yes,because computed t is less than the critical value.
C)No,because computed t lies in the region of acceptance.
D)No,because 217.24 is quite close to 216.

Question 46

If the 1% level of significance is used and the computed value of z is +6.00,what is our decision?

A)Do not reject H₀
B)Reject H₀
C)Reject H₁
D)None of these

Question 47

The standard normal distribution is the appropriate distribution when testing a hypothesis about a population proportion.

Question 48

What is the critical value for a one-tailed hypothesis test in which a null hypothesis is tested at the 5% level of significance based on a sample size of 25?

A)1.708
B)1.711
C)2.060
D)2.064

Question 49

What do we call the statement that determines if the null hypothesis is rejected?

A)Decision rule
B)Test statistic
C)Alternate hypothesis
D)Critical value

Question 50

Test at the 0.01 level the statement that 55% of those families who plan to purchase a vacation residence in Florida want a condominium.The null hypothesis is $\pi$ = 0.55 and the alternate is .A random sample of 400 families who planned to buy a vacation residence revealed that 228 families want a condominium.What decision should be made regarding the null hypothesis?

A)Do not reject it
B)Reject it
C)Cannot accept nor reject it based on the information given
D)None of these

Question 51

A machine is set to fill the small size packages of M&M candies with 56 candies per bag.A sample revealed: 3 bags of 56,2 bags of 57,1 bag of 55,and 2 bags of 58.How many degrees of freedom are there?

A)9
B)1
C)8
D)7

Question 52

The mean length of a small counter balance bar is 43 millimeters.There is concern that the adjustments of the machine producing the bars have changed.Test the claim at the 0.02 level that there has been no change in the mean length.The alternate hypothesis is that there has been a change.Twelve bars (n = 12)were selected at random and their lengths recorded.The lengths are (in millimeters)42,39,42,45,43,40,39,41,40,42,43 and 42.The mean of the sample is 41.5 and the standard deviation 1.784.Computed t = -2.913.Has there been a statistically significant change in the mean length of the bars?

A)Yes,because the computed t lies in the rejection region.
B)No,because the information given is not complete.
C)No,because the computed t lies in the area to the right of -2.718.
D)Yes,because 43 is greater than 41.5.

Question 53

When testing population proportions,the z statistic can be used when n $\pi$ and n(1 - $\pi$ )are greater than five.

Question 54

A sample proportion is found by dividing the number of successes in the sample by the number sampled.

Question 55

A random sample of size 15 is selected from a normal population.The population standard deviation is unknown.Assume that a two-tailed test at the 0.10 significance level is to be used.For what value of t will the null hypothesis not be rejected?

A)To the left of -1.282 or to the right of 1.282
B)To the left of -1.345 or to the right of 1.345
C)Between -1.761 and 1.761
D)To the left of -1.645 or to the right of 1.645

Question 56

What is a Type II error?

A)Accepting a false null hypothesis
B)Rejecting a false null hypothesis
C)Accepting a false alternate hypothesis
D)Rejecting a false alternate hypothesis

Question 57

To conduct a test of hypothesis with a small sample,we need to be able to make an assumption that:

A)a larger computed value of t will be needed to reject the null hypothesis.
B)the region of acceptance will be wider than for large samples.
C)the confidence interval will be wider than for large samples.
D)the population is normally distributed.

Question 58

A manufacturer wants to increase the absorption capacity of a sponge.Based on past data,the average sponge could absorb 3.5 ounces.After the redesign,the absorption amounts of a sample of sponges were (in ounces): 4.1,3.7,3.3,3.5,3.8,3.9,3.6,3.8,4.0,and 3.9.What is the decision rule at the 0.01 level of significance to test if the new design increased the absorption amount of the sponge?

A)Do not reject null hypothesis if computed t is less than 2.580
B)Do not reject null hypothesis if computed t is less than 2.821
C)Reject null hypothesis if computed z is 1.96 or larger
D)Reject null hypothesis if computed t is less than 2.764

Question 59

A null hypothesis makes a claim about a

A)Population parameter
B)Sample statistic
C)Sample mean
D)Type II error

Question 60

What are the two critical values for a two-tailed test with a 0.01 level of significance when n is large and the population standard deviation is known?

A)Above 1.96 and below -1.96
B)Above 1.65 and below -1.65
C)Above 2.58 and below -2.58
D)Above 1.00 and below -1.00

Question 61

If the critical z-value for a test statistic equals 2.45,what value of the test statistic would provide the least chance of making a Type I error?

A)3.74
B)10,000
C)2.46
D)4.56

Question 62

The average cost of tuition,room and board at small private liberal arts colleges is reported to be $8,500 per term,but a financial administrator believes that the average cost is higher.A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745 with a standard deviation of $1,200.Let = 0.05.What are the null and alternative hypotheses for this study?

A)Null: µ $\le$ $9,000;alternative: µ > $9,000
B)Null: µ $\ge$ $9,000;alternative: µ < $9,000
C)Null: µ $\le$ $8,500;alternative: µ > $8,500
D)Null: µ $\ge$ $8,500;alternative: µ < $8,500

Question 63

For a two-tailed test with a 0.05 significance level,what is the rejection region when n is large and the population standard deviation is known?

A)Between $\pm$ 1.96
B)Between $\pm$ 1.65
C)Greater than +1.96 and less than -1.96
D)Greater than +1.65 and less than -1.65

Question 64

Which of the following is NOT one of the five steps in the hypothesis testing procedure?

A)Formulate a decision rule
B)State the null and alternate hypotheses
C)Select a level for $\beta$
D)Identify the test statistic

Question 65

What is another name for the alternate hypothesis?

A)Null hypothesis
B)Hypothesis of no difference
C)Rejected hypothesis
D)Research hypothesis

Question 66

The average cost of tuition,room and board at small private liberal arts colleges is reported to be $8,500 per term,but a financial administrator believes that the average cost is higher.A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745 with a standard deviation of $1,200.Let = 0.05.What is the test statistic for this test?

A) $\pm$ 3.82
B)0.204
C)-3.82
D)+3.82

Question 67

If 20 out of 50 students sampled live in a college dormitory,what is the estimated proportion of students at the University living in a dormitory?

A)0.20
B)0.40
C)0.50
D)0.60

Question 68

A manufacturer of stereo equipment introduces new models in the fall.Retail dealers are surveyed immediately after the Christmas selling season regarding their stock on hand of each piece of equipment.It has been discovered that unless 40% of the new equipment ordered by the retailers in the fall had been sold by Christmas,immediate production cutbacks are needed.The manufacturer has found that contacting all of the dealers after Christmas by mail is frustrating as many of them never respond.This year 80 dealers were selected at random and telephoned regarding a new receiver.It was discovered that 38% of those receivers had been sold.Since 38% is less than 40%,does this mean that immediate production cutbacks are needed or can this difference of 2 percentage points be attributed to sampling? Test at the 0.05 level.Computed z = -0.37.

A)Cut back production
B)Do not cut back production
C)Cannot determine based on information given
D)None of these

Question 69

If we reject the null hypothesis what can we conclude subject to the $\alpha$ risk?

A)Null hypothesis is false
B)Alternative hypothesis is false
C)Null hypothesis is true
D)Both the null hypothesis and the alternative hypothesis are true
E)Both the null hypothesis and the alternative hypothesis are false

Question 70

What are the critical z-values for a two-tailed hypothesis test if $\alpha$ = 0.01?

A) $\pm$ 1.96
B) $\pm$ 2.33
C) $\pm$ 2.58
D) $\pm$ 1.65

Question 71

The sample proportion is defined as:

A)n $\pi$
B)x/n
C)n!
D) $\pi$

Question 72

The average cost of tuition,room and board at small private liberal arts colleges is reported to be $8,500 per term,but a financial administrator believes that the average cost is higher.A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745 with a standard deviation of $1,200.Let = 0.05.What is the critical z-value for this test?

A)+1.96
B)-1.96
C)+ 1.65
D)-1.65

Question 73

Which symbol is a test statistic used to test a hypothesis about a population mean?

A) $\alpha$
B) $\beta$
C) $\mu$
D)z

Question 74

The average cost of tuition,room and board at small private liberal arts colleges is reported to be $8,500 per term,but a financial administrator believes that the average cost is higher.A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745 with a standard deviation of $1,200.Let = 0.05.What is the p-value for this test?

A)0.0000
B)0.0124
C)0.0500
D)0.4938

Question 75

The claim that "40% of those persons who retired from an industrial job before the age of 60 would return to work if a suitable job was available," is to be investigated at the 0.02 level of risk.If 74 out of the 200 workers sampled said they would return to work,what is our decision?

A)Do not reject the null hypothesis because -0.866 lies in the region between 0 and -2.33
B)Do not reject the null hypothesis because -0.866 lies in the region between 0 and -2.58
C)Reject the null hypothesis because 37% is less than 40%
D)Do not reject the null hypothesis because 37% lies in the area between 0% and 40%

Question 76

The number of trials and the population proportion are respectively represented by what symbols?

A)p and n
B)
C)z and t
D)n and $\pi$

Question 77

What is the probability of making a Type II error if the null hypothesis is actually true?

A) $\alpha$
B)1
C)0
D)0.05

Question 78

In hypothesis testing,what is the level of significance?

A)Risk of rejecting the null hypothesis when it is true
B)Symbolized by the Greek letter " $\alpha$ "
C)Value between 0 and 1
D)Selected before a decision rule can be formulated
E)All of these are true

Question 79

For a one-tailed hypothesis test,the critical z-value of the test statistic is -2.33.Which of the following is true about the hypothesis test?

A) $\alpha$ = 0.05 for a lower-tailed test
B) $\alpha$ = 0.01 for a lower-tailed test
C) $\alpha$ = 0.05 for an upper-tailed test
D) $\alpha$ = 0.01 for an upper-tailed test

Question 80

For a hypothesis test with an alternative hypothesis: µ > 6,700,where is the rejection region for the hypothesis test located?

A)Both tails
B)Left or lower tail
C)Right or upper tail
D)Center