Statistical hypotheses testing: Hypotheses testing is used to make inferences about the population based on the sample data. The hypotheses test consists of null hypothesis and alternative hypothesis.
Null hypothesis: The null hypothesis states that there is no difference in the test, which is denoted by . Moreover, the sign of null hypothesis is equal , greater than or equal and less than or equal .
Alternative hypothesis: The hypothesis that differs from is called alternative hypothesis. This signifies that there is a significant difference in the test. The sign of alternative hypothesis is less than , greater than , or not equal .
Proportion: The ratio of the number of favorable outcomes and total number of possible outcomes in the sample called as the proportion.
Z-statistic for proportion: The standardized z- statistic is defined as the ratio of the ‘distance of the observed statistic from the proportion of the null distribution’ and the ‘standard deviation of the null distribution’.
P-value: The probability of getting the value of the statistic that is as extreme as the observed statistic when the null hypothesis is true is called as P-value. Therefore, it assumes “null hypothesis is true”.
The formula for sample proportion is,
Where x is the number of success in the sample and n is the total sample size.
The formula for population proportion is,
Where X is the number of success in the population and N is the total population size.
The test statistic for one proportion is,
Here,
The formula for the p-value for right-sided test is,
Procedure for finding the probability is listed below:
1.From the table of standard normal distribution, locate the z-value
2.Move left until the first column is reached.
3.Move upward until the top row is reached.
4.Locate the probability value, by the intersection of the row and column values gives the area to the left of z.
The Melodic Kortholt Company will change its current health plan if at least half...continues
The Melodic Kortholt Company will change its current health plan if at least half the employees are dissatisfied with it. A trial sample of 25 employees shows that 16 are dissatisfied. The p-value for a right-tailed test is a. 0.4192 b. 0.1337 c. 0.0808 d. 0.0901
The Melodic Kortholt Company will change its current health plan if at least half the employees are dissatisfied with it. A trial sample of 25 employees shows that 16 are dissatisfied. The p-value for a right-tailed test is: О .0808 0 0901 1337 О .4192
24) The Melodic Kortholt Company will change its current health plan if at least half the employees are dissatisfied with it. A trial sample of 25 employees shows that 16 are dissatisfied. The p-value for a right-tailed test is 24) ______ A) .0901 B) .0808 C) .4192 D) .1337
Randi wants to know if at least 90% of the employees at her company are currently enrolled in a health insurance plan. She randomly samples 500 employees and finds that 459 of them are currently enrolled in a plan. Randi conducts a one-proportion hypothesis test at the 5% significance level, to test whether the true proportion of employees enrolled in a plan at this company is greater than 90%. For this test: H0:p=0.9; Ha:p>0.9, which is a right-tailed test. Use...
Proctor & Gamble claims that at least half the bars of Ivory soap they produce are 99.44% pure (or more pure) as advertised. Unilever, one of Proctor & Gamble's competitors, wishes to put this claim to the test. They sample the purity of 105 bars of Ivory soap. They find that 49 of them meet the 99.44% purity advertised. What type of test should be run? Ot-test of a mean Oz-test of a proportion The alternative hypothesis indicates a O...
A company wants to determine if its employees have any preference among 5 different health plans. A sample of 200 employees provided the data below. Test the claim that there is no preference. Use α = 0.01. Two decimal places. Plan 1 2 3 4 5 Employees 30 65 18 32 55
a.) The cost of Canada's health care system continues to escalate, increasing the tax burden for all citizens. A study fo 70 Canadians showed a sample mean health care expenditure of $5170. Assume the expenditure for a randomly selected Canadian is normally distributed, with a population standard deviation of $687. Calculate the margin of error for a 99% confidence interval estimate of the population mean health care expenditure. b.) A clinic in rural Guatemala measures the blood calcium level of...
A company wants to determine if its employees have any preference among 5 different health plans which it offers to them. A sample of 200 employees provided the data below. Calculate the chi-square test statistic xã to test the claim that the probabilities show no preference. Use a = 0.01. 3 4 5 Plan 1 2 Employees 32 18 55 65 30 A. 55.63 OB. 37.45 O c. 48.91 OD. 45.91
(7 points) Suppose a recent random sample of employees nationwide that have a 401(k) retirement plan found that 20% of them had borrowed against it in the last year. A local company is interested in assessing whether this proportion adequately describes the borrowing behavior of their employees. They take a random sample of 150 employees and find that 17 had borrowed from their plan. Conduct a hypothesis test to investigate whether the borrowing rate at this company is less than...
A Deloitte employment survey asked a sample of human resource executives how their company planned to change its workforce over the next 12 months. A categorical response variable showed three options: the company plans to hire and add to the number of employees, the company plans no change in the number of employees, or the company plans to lay off and reduce the number of employees. Another categorical variable indicated if the company was private or public. Sample data for...