
Concept explainers
Parameters and hypotheses For each of the following situations, define the parameter (proportion or mean) and write the null and alternative hypotheses in terms of parameter values. Example: We want to know if the proportion of up days in the stock market is 50%. Answer: Let p = the proportion of up days. H0: p = 0.5 vs. HA: p ≠ 0.5.
- a) A casino wants to know if their slot machine really delivers the 1 in 100 win rate that it claims.
- b) Last year, customers spent an average of $35.32 per visit to the company’s website. Based on a random sample of purchases this year, the company wants to know if the mean this year has changed.
- c) A pharmaceutical company wonders if their new drug has a cure rate different from the 30% reported by the placebo.
- d) A bank wants to know if the percentage of customers using their website has changed from the 40% that used it before their system crashed last week.
a.

Define the parameter.
State the null and alternative hypotheses.
Answer to Problem 1E
The parameter is p, which is defined as the probability of winning on a slot machine.
The test hypotheses are given below:
Null hypothesis:H0:p=0.01_
Alternative hypothesis:HA:p≠0.01_
Explanation of Solution
Justification:
Parameter:
Any statistical measure based on all units in the population is called Parameter.
The study based on the casino wants to identify the probability of winning on a slot machine.
In the given situation, the parameter of interest is p, which is defined as the probability of winning on a slot machine.
Hypotheses:
The test hypotheses are given below:
Null hypothesis:
H0:p=0.01
That is, the proportion of winning on a slot machine is 0.01
Alternative hypothesis:
HA:p≠0.01
That is, the proportion of winning on a slot machine is different from 0.01.
b.

Define the parameter.
State null and alternative hypothesis.
Answer to Problem 1E
The parameter is μ, which is defined as the average amount spent on purchase per customer in a year.
The test hypotheses are:
Null hypothesis: H0:μ=$35.32_
Alternative hypothesis: HA:μ≠$35.32_
Explanation of Solution
Justification:
The data represents the amount spent on purchase by the customer.
In the given situation, the parameter of interest is μ, which is defined as the average amount spent on purchase per customer in a year.
The test hypotheses are given below:
Null hypothesis: H0:μ=$35.32_
That is, the average amount spent on purchase per customer in a year is $35.32.
Alternative hypothesis: HA:μ≠$35.32_
That is, the average amount spent on purchase per customer in a year is different from $35.32.
c.

Define the parameter.
State null and alternative hypothesis.
Answer to Problem 1E
The parameter is p, which is defined as the percentage of patients cured by new drug.
The test hypotheses are given below:
Null hypothesis: H0:p=0.30_
Alternative hypothesis: HA:p≠0.30_
Explanation of Solution
Justification:
The data represents the effect of new drug on patients by pharmaceutical company.
In the given situation, the parameter of interest is p, which is defined as the percentage of patients cured by new drug.
The test hypotheses are given below:
Null hypothesis: H0:p=0.30_
That is, the percentage of patients cured by new drug is 0.30.
Alternative hypothesis: HA:p≠0.30_
That is, the percentage of patients cured by new drug is different from 0.30.
d.

Define the parameter.
State null and alternative hypothesis.
Answer to Problem 1E
The parameter is p, which is defined as the percentage of Customers using the website of bank.
The test hypotheses are given below:
Null hypothesis: H0:p=0.40_
Alternative hypothesis: HA:p≠0.40_
Explanation of Solution
Justification:
A bank wants to identify the proportion of customers using the bank’s website.
In the given situation, the parameter of interest is p, which is defined as the percentage of Customers using the website of bank.
The test hypotheses are given below:
Null hypothesis: H0:p=0.40_
That is, the percentage of Customers using the website of bank is 40%.
Alternative hypothesis: HA:p≠0.40_
That is, the percentage of Customers using the website of bank is different from 40%.
Want to see more full solutions like this?
Chapter 19 Solutions
Intro Stats
- ian income of $50,000. erty rate of 13. Using data from 50 workers, a researcher estimates Wage = Bo+B,Education + B₂Experience + B3Age+e, where Wage is the hourly wage rate and Education, Experience, and Age are the years of higher education, the years of experience, and the age of the worker, respectively. A portion of the regression results is shown in the following table. ni ogolloo bash 1 Standard Coefficients error t stat p-value Intercept 7.87 4.09 1.93 0.0603 Education 1.44 0.34 4.24 0.0001 Experience 0.45 0.14 3.16 0.0028 Age -0.01 0.08 -0.14 0.8920 a. Interpret the estimated coefficients for Education and Experience. b. Predict the hourly wage rate for a 30-year-old worker with four years of higher education and three years of experience.arrow_forward1. If a firm spends more on advertising, is it likely to increase sales? Data on annual sales (in $100,000s) and advertising expenditures (in $10,000s) were collected for 20 firms in order to estimate the model Sales = Po + B₁Advertising + ε. A portion of the regression results is shown in the accompanying table. Intercept Advertising Standard Coefficients Error t Stat p-value -7.42 1.46 -5.09 7.66E-05 0.42 0.05 8.70 7.26E-08 a. Interpret the estimated slope coefficient. b. What is the sample regression equation? C. Predict the sales for a firm that spends $500,000 annually on advertising.arrow_forwardCan you help me solve problem 38 with steps im stuck.arrow_forward
- How do the samples hold up to the efficiency test? What percentages of the samples pass or fail the test? What would be the likelihood of having the following specific number of efficiency test failures in the next 300 processors tested? 1 failures, 5 failures, 10 failures and 20 failures.arrow_forwardThe battery temperatures are a major concern for us. Can you analyze and describe the sample data? What are the average and median temperatures? How much variability is there in the temperatures? Is there anything that stands out? Our engineers’ assumption is that the temperature data is normally distributed. If that is the case, what would be the likelihood that the Safety Zone temperature will exceed 5.15 degrees? What is the probability that the Safety Zone temperature will be less than 4.65 degrees? What is the actual percentage of samples that exceed 5.25 degrees or are less than 4.75 degrees? Is the manufacturing process producing units with stable Safety Zone temperatures? Can you check if there are any apparent changes in the temperature pattern? Are there any outliers? A closer look at the Z-scores should help you in this regard.arrow_forwardNeed help pleasearrow_forward
- Please conduct a step by step of these statistical tests on separate sheets of Microsoft Excel. If the calculations in Microsoft Excel are incorrect, the null and alternative hypotheses, as well as the conclusions drawn from them, will be meaningless and will not receive any points. 4. One-Way ANOVA: Analyze the customer satisfaction scores across four different product categories to determine if there is a significant difference in means. (Hints: The null can be about maintaining status-quo or no difference among groups) H0 = H1=arrow_forwardPlease conduct a step by step of these statistical tests on separate sheets of Microsoft Excel. If the calculations in Microsoft Excel are incorrect, the null and alternative hypotheses, as well as the conclusions drawn from them, will be meaningless and will not receive any points 2. Two-Sample T-Test: Compare the average sales revenue of two different regions to determine if there is a significant difference. (Hints: The null can be about maintaining status-quo or no difference among groups; if alternative hypothesis is non-directional use the two-tailed p-value from excel file to make a decision about rejecting or not rejecting null) H0 = H1=arrow_forwardPlease conduct a step by step of these statistical tests on separate sheets of Microsoft Excel. If the calculations in Microsoft Excel are incorrect, the null and alternative hypotheses, as well as the conclusions drawn from them, will be meaningless and will not receive any points 3. Paired T-Test: A company implemented a training program to improve employee performance. To evaluate the effectiveness of the program, the company recorded the test scores of 25 employees before and after the training. Determine if the training program is effective in terms of scores of participants before and after the training. (Hints: The null can be about maintaining status-quo or no difference among groups; if alternative hypothesis is non-directional, use the two-tailed p-value from excel file to make a decision about rejecting or not rejecting the null) H0 = H1= Conclusion:arrow_forward
- Please conduct a step by step of these statistical tests on separate sheets of Microsoft Excel. If the calculations in Microsoft Excel are incorrect, the null and alternative hypotheses, as well as the conclusions drawn from them, will be meaningless and will not receive any points. The data for the following questions is provided in Microsoft Excel file on 4 separate sheets. Please conduct these statistical tests on separate sheets of Microsoft Excel. If the calculations in Microsoft Excel are incorrect, the null and alternative hypotheses, as well as the conclusions drawn from them, will be meaningless and will not receive any points. 1. One Sample T-Test: Determine whether the average satisfaction rating of customers for a product is significantly different from a hypothetical mean of 75. (Hints: The null can be about maintaining status-quo or no difference; If your alternative hypothesis is non-directional (e.g., μ≠75), you should use the two-tailed p-value from excel file to…arrow_forwardPlease conduct a step by step of these statistical tests on separate sheets of Microsoft Excel. If the calculations in Microsoft Excel are incorrect, the null and alternative hypotheses, as well as the conclusions drawn from them, will be meaningless and will not receive any points. 1. One Sample T-Test: Determine whether the average satisfaction rating of customers for a product is significantly different from a hypothetical mean of 75. (Hints: The null can be about maintaining status-quo or no difference; If your alternative hypothesis is non-directional (e.g., μ≠75), you should use the two-tailed p-value from excel file to make a decision about rejecting or not rejecting null. If alternative is directional (e.g., μ < 75), you should use the lower-tailed p-value. For alternative hypothesis μ > 75, you should use the upper-tailed p-value.) H0 = H1= Conclusion: The p value from one sample t-test is _______. Since the two-tailed p-value is _______ 2. Two-Sample T-Test:…arrow_forwardPlease conduct a step by step of these statistical tests on separate sheets of Microsoft Excel. If the calculations in Microsoft Excel are incorrect, the null and alternative hypotheses, as well as the conclusions drawn from them, will be meaningless and will not receive any points. What is one sample T-test? Give an example of business application of this test? What is Two-Sample T-Test. Give an example of business application of this test? .What is paired T-test. Give an example of business application of this test? What is one way ANOVA test. Give an example of business application of this test? 1. One Sample T-Test: Determine whether the average satisfaction rating of customers for a product is significantly different from a hypothetical mean of 75. (Hints: The null can be about maintaining status-quo or no difference; If your alternative hypothesis is non-directional (e.g., μ≠75), you should use the two-tailed p-value from excel file to make a decision about rejecting or not…arrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin HarcourtHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL



