Purchase Solution

Hypothesis testing using either t or normal distribution

Not what you're looking for?

Ask Custom Question

1. A sample of 49 observations is selected from a normal population. The sample mean is 21, and the population standard deviation is 4. Conduct the following test of hypothesis using the 0.05 significance level.

H0 : μ ≤ 20
H1 : μ > 20

a. Is this a one- or two-tailed test?

"One-tailed"-the alternate hypothesis is greater than direction.
"Two-tailed"-the alternate hypothesis is different from direction.

b. What is the decision rule? (Round your answer to 3 decimal places.)

H0, when z >

c. What is the value of the test statistic? (Round your answer to 2 decimal places.)

Value of the test statistic

d. What is your decision regarding H0?

Reject
Do not reject

There is evidence to conclude that the population mean is greater than 20.

e. What is the p-value? (Round your answer to 4 decimal places.)

p-value

2. At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden was told, "You can average $89 a day in tips." Assume the population of daily tips is normally distributed with a standard deviation of $2.81. Over the first 40 days she was employed at the restaurant, the mean daily amount of her tips was $92.66. At the 0.01 significance level, can Ms. Brigden conclude that her daily tips average more than $89?

a. State the null hypothesis and the alternate hypothesis.

H0: μ ≥ 89 ; H1: μ < 89
H0: μ ≤ 89 ; H1: μ > 89
H0: μ = 89 ; H1: μ ≠ 89
H0: μ >89 ; H1: μ = 89

b. State the decision rule.

Reject H1 if z > 2.33
Reject H0 if z < 2.33
Reject H0 if z > 2.33
Reject H1 if z < 2.33

c. Compute the value of the test statistic. (Round your answer to 2 decimal places.)

Value of the test statistic

d. What is your decision regarding H0?

Reject H0
Do not reject H0

e. What is the p-value? (Round your answer to 4 decimal places.)

p-value

3. The Rocky Mountain district sales manager of Rath Publishing Inc., a college textbook publishing company, claims that the sales representatives make an average of 41 sales calls per week on professors. Several reps say that this estimate is too low. To investigate, a random sample of 25 sales representatives reveals that the mean number of calls made last week was 43. The standard deviation of the sample is 2.8 calls. Using the 0.010 significance level, can we conclude that the mean number of calls per salesperson per week is more than 41?

H0 : μ ≤ 41
H1 : μ > 41

1. Compute the value of the test statistic. (Round your answer to 3 decimal places.)

Value of the test statistic

4. A United Nations report shows the mean family income for Mexican migrants to the United States is $26,580 per year. A FLOC (Farm Labor Organizing Committee) evaluation of 26 Mexican family units reveals a mean to be $38,900 with a sample standard deviation of $11,054. Does this information disagree with the United Nations report? Apply the 0.01 significance level.

a. State the null hypothesis and the alternate hypothesis.

5. The following information is available
H0: μ =

H1: μ ≠

b. State the decision rule for .01 significance level. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

Reject H0 if t is not between
and

c. Compute the value of the test statistic. (Round your answer to 2 decimal places.)

Value of the test statistic

5. The following information is available.
H0 : μ ≥ 220

H1 : μ < 220

A sample of 64 observations is selected from a normal population. The sample mean is 215, and the population standard deviation is 15. Conduct the following test of hypothesis using the .025 significance level.

a. Is this a one- or two-tailed test?

Two-tailed test
One-tailed test

b. What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

H0 when z <

c. What is the value of the test statistic? (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

Value of the test statistic

d. What is your decision regarding H0?

Reject
Do not reject

e. What is the p-value? (Round your answer to 4 decimal places.)

p-value

6. Given the following hypotheses:

H0 : μ ≤ 10
H1 : μ > 10

A random sample of 10 observations is selected from a normal population. The sample mean was 12 and the sample standard deviation 3. Using the .05 significance level:

a. State the decision rule. (Round your answer to 3 decimal places.)

Reject H0 if t >

b. Compute the value of the test statistic. (Round your answer to 3 decimal places.)

Value of the test statistic

7. Given the following hypotheses:

H0 : μ = 400

H1 : μ ≠ 400

A random sample of 12 observations is selected from a normal population. The sample mean was 407 and the sample standard deviation 6. Using the .01 significance level:

a. State the decision rule. (Negative amount should be indicated by a minus sign. Round your answers to 3 decimal places.)

Reject H0 when the test statistic is the interval (
,
).

b. Compute the value of the test statistic. (Round your answer to 3 decimal places.)

Value of the test statistic

Purchase this Solution
Solution Summary

The solution gives detailed solutions to a series of questions on hypothesis testing using either t or normal distribution following formal 5 steps.

Solution Preview

Please check attachment

1. A sample of 49 observations is selected from a normal population. The sample mean is 21, and the population standard deviation is 4. Conduct the following test of hypothesis using the 0.05 significance level.
H0 : μ ≤ 20
H1 : μ > 20
a. Is this a one- or two-tailed test?
"One-tailed"-the alternate hypothesis is greater than direction.
"Two-tailed"-the alternate hypothesis is different from direction.
b. What is the decision rule? (Round your answer to 3 decimal places.)
H0, when z >1.645
c. What is the value of the test statistic? (Round your answer to 2 decimal places.)
Value of the test statistic=(21-20)/[4/sqrt(49)]=1.75
d. What is your decision regarding H0?
Reject
Do not reject
There is evidence to conclude that the population mean is greater than 20.
e. What is the p-value? (Round your answer to 4 decimal places.)
p-value=P(Z>1.75)=0.0401
2. At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden was told, "You can average $89 a day in tips." Assume the population of daily tips is normally distributed with a standard deviation of $2.81. Over the first 40 days she was employed at the restaurant, the mean daily amount of her tips was $92.66. At the 0.01 significance level, can Ms. Brigden conclude that her daily tips average more than $89?
a. State the ...

Purchase this Solution
Free BrainMass Quizzes
Measures of Central Tendency

Tests knowledge of the three main measures of central tendency, including some simple calculation questions.

Know Your Statistical Concepts

Each question is a choice-summary multiple choice question that presents you with a statistical concept and then 4 numbered statements. You must decide which (if any) of the numbered statements is/are true as they relate to the statistical concept.

Measures of Central Tendency

This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.

Terms and Definitions for Statistics

This quiz covers basic terms and definitions of statistics.

View More Free Quizzes
Related BrainMass Solutions

  • five step process for hypothesis testing

    The choice generally remains between normal and t- distribution.

  • Test of Hypothesis with Significance Level Provided

    table Normal distribution, z table Sample size is 30 or less and we assume that the population is normal or approximately so Normal distribution, z table t distribution, t table We can use t -test if the sample size is less than 30

  • Perform hypothesis testing on one variable's data

    238860 Perform hypothesis testing on one variable's data Perform hypothesis testing on one variable's data. (Choose either the intrinsic or extrinsic column.)

  • Statistics: Using the Wrong Distribution

    If the standard normal distribution is incorrectly used instead, does that mistake make you more or less likely to reject the null hypothesis, or does it not make a difference? Explain.

  • Normal Distribution, Testing of Hypothesis

    = M +t*sx= 3.54 =3.5+2.1314*0.02 Lower acceptance limit= M -t*sx= 3.46 =3.5-2.1314*0.02 Accept Null Hypothesis since the sample mean is within acceptance region Answers multiple choice questions on Normal Distribution, Testing of

  • Statistics - Hypothesis Test for one Variable - T-test

    215982 Hypothesis test for one variable: t-test. Using AIU's large database of survey responses from the AIU data set, complete the following: Perform hypothesis testing on one variable's data. (Choose either the intrinsic or extrinsic column.)

  • Hypothesis Testing: Internet Usage for a Company

    ● Using alpha = .05, and a t distribution, graph the rejection region. ● Conclude whether to reject or not to reject the null hypothesis. ● Does your statistical analysis support the author's statement?

  • Hyplthesis Testing of Mean & Proportion

    Define the rejection region using either the P-value method or critical values from the Normal distribution. 6. Make a decision to reject or fail to reject the null hypothesis. 7. Interpret the decision in the context of the original claim.

  • Hypothesis Testing in Hockey Players

    b) Identify the sampling distribution to be used: the standard normal distribution or the Student's t distribution. Find the critical value(s). c) Compute the z or t value of the sample test statistic.

  • Paired Difference Test

    The above problem can also be computed using the Student's t distribution without approximating the test statistic to a Standard normal distribution.

View More Related Solutions