**Educational Website Text: Hypothesis Testing Example****Scenario:**Executives of a supermarket chain aim to understand the average time customers spend shopping during their visits. The average time, represented as μ, has been previously reported as 38 minutes. However, executives suspect that this might not be accurate and opt for a statistical test to verify their hypothesis. A statistical consultant is hired for this purpose.**Data Collection:**The consultant takes a random sample of shopping times. The sample shows a mean time of 44 minutes, with a standard deviation of 10 minutes.**Tasks:**Based on this information, address the following:**(a) Hypothesis Formulation:**- Null Hypothesis (H₀): μ = 38 (The mean shopping time is 38 minutes)- Alternative Hypothesis (H₁): μ ≠ 38 (The mean shopping time is different from 38 minutes)**(b) Decision Making and Errors:**- If the consultant decides not to reject the null hypothesis, she might be making a **Type II error**. This occurs when the null hypothesis is not rejected, although it is false.**(c) Type I Error Description:**- A Type I error involves **rejecting** the hypothesis that μ is **38 minutes** when, in fact, μ is **38 minutes**. This error happens when a true null hypothesis is incorrectly rejected.

Answered: Executives of a supermarket chain are…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Similar questions

Is it possible for the standard deviation of a dataset to be larger than its variance? Explain mathematically. Give an example to explain the above statement.
On average, a coffee machine fills into 214 milliliter cups. Sometimes, the machine makes errors with an estimated variance of 81. What is the standardized score for a randomly selected coffee cup that measured 250 milliliters? Answer:
???
The life span in Honolulu is approximately normally distributed. The mean life span is 77 years. A foreign newspaper claims that the mean lifespan for Honolulu residents is less than 77 years. You randomly select a sample of 20 obituary notices in a Honolulu newspaper. The table below shows the data collected (in years). 72 68 81 93 56 19 78 94 83 84 77 69 85 97 75 71 86 47 66 27 Test the foreign newspaper's claim using a = 0.01. There is enough evidence to reject the null hypothesis. The claim is true. There is enough evidence to reject the null hypothesis. The claim is false. There is not enough evidence to reject the null hypothesis. The claim is probably true. There is not enough evidence to reject the null hypothesis. The claim is probably false.
The systolic blood pressure of individuals is thought to be related to both age and weight. Let the systolic blood pressure, age, and weight be represented by the variables x1, x2, and x3, respectively. Suppose that Minitab was used to generate the following descriptive statistics, correlations, and regression analysis for a random sample of 15 individuals. Descriptive Statistics Variable N Mean Median TrMean StDev SE Mean x1 15 158.42 158.72 158.42 3.127 0.807388 x2 15 65.95 66.45 65.95 1.091 0.281695 x3 15 187.23 186.63 187.23 4.171 1.076948 Variable Minimum Maximum Q1 Q3 x1 124 174 135.828 166.400 x2 41 80 47.088 77.579 x3 124 244 142.885 223.525 Correlations (Pearson) x1 x2 x2 0.829 x3 0.860 0.661 Regression Analysis The regression equation is x1 = 0.837 + 1.120x2 + 0.928x3 Predictor Coef StDev T P…
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Students applying to graduate schools in many disciplines are required to take the Graduate Record Examination (GRE). An ambitious undergraduate student creates a study program that she believes will greatly increase students’ GRE scores, relative to the general population. She recruits a sample of 36 students believed to be representative of the larger undergraduate student population and puts them through the study program. Afterwards, they complete the GRE and receive a mean score of M = 1052. The GRE is normally distributed in the general population with a mean of μ = 1000 and a standard deviation of σ = 150. a) Using the data provided above, calculate and interpret the effect size, Cohen’s d. b) Given the results of the analysis and the associated effect size, do you think this study program was a very effective way to change GRE score outcomes? Why or why not?
A baker keeps count of the number of doughnuts sold each day for consecutive selected 15 days. The numbers are (b) 135 147 134 146 155 155 141 135 147 151 147 175 151 156 147 (i) (1i) (ii1) Find the median. (iv) Find the mode. Find the mean. Find the standard deviation.
The incomes of math tutors in a tutoring center of a university are normally distributed with a mean of $1100 and a standard deviation of $150 what percentage of tutors earn less than $900 a month
A local authority is going to study the relationship between the size of household and the daily plastic usage consumed by them. The results of a sampling given below in Table 5 indicate some values of X (weight of plastic usage) and Y (the size of household). Table 5: Weight of plastic usage (X) and size of household (Y) X 0.27 1.41 2.19 | 2.83 2.19 1.81 0.85 3.05 Y 2 3 3 4 2 1 5 i) From the above sampling, find the value of correlation coefficient r. ii) Using the same sample data set above, conduct the hypothesis testing to know whether the variable X and Y are really correlates using 95% confidence level. iii) Find out if the decision in (ii) may change if you increase the confidence level to 99%.
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