1. A lightbulb manufacturer has developed a new lightbulb that it claims has an average life of more than 1,000 hours. State the null hypothesis (Ho) and alternative hypothesis (Ha) that will be used to verify this claim.
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- Lightbulbs of a certain type are advertised as having an average lifetime of 750 hours. The price of these bulbs is very favorable, so a potential customer has decided to go ahead with purchase arrangement unless it can be conclusively demonstrated that the true average lifetime is smaller than what is advertised. A random sample of 44 bulbs was selected, the lifetime of each bulb determined, and the appropriate hypotheses were tested using MINITAB, resulting in the accompanying output. Variable N lifetime 44 St Dev 38.19 What conclusion would be appropriate for a significance level of 0.05? Mean 738.44 SEMean 5.76 Z -2.01 P-Value 0.022 Reject the null hypothesis. There is sufficient evidence to conclude that the lifetime of a bulb is less than 750 hours. O Do not reject the null hypothesis. There is sufficient evidence to conclude that the lifetime of a bulb is less than 750 hours. O Do not reject the null hypothesis. There is not sufficient evidence to conclude that the lifetime of a…A random sample of 24 local sociology graduates scored an average of 460 on the GRE advanced sociology test, with a standard deviation of 22. We wonder if this significantly different from the national average (µ = 445). a) Evaluate assumptions if we can use a t-test and summarize parameters and statistics. b) State the null hypothesis (i.e., H0) and the working hypothesis (i.e., H1). c) Establish the critical region for t-distributions at α=0.05 with a two-tailed test. d) Compute the test statistics (i.e., tobtained) and the corresponding probability (i.e., pvalue). e) Make a decision and interpret test results.A consumer group plans a comparative study of the mean life of four different brands of batteries. Ten batteries of each brand will be randomly selected and the time until the energy level falls below a pre-specified level is measured. a) Which of the following is the appropriate alternative hypothesis for the null hypothesis: H0: μa = μb = μc = μd? (In this problem, μa = mean time of Brand A, μb = mean time of Brand B, etc.) Ha: none of the means are equal Ha: μa ≠ μb ≠ μc ≠ μd Ha: μa ≠ μb, μa ≠ μc, μa ≠ μd, μb ≠ μc, μb ≠ μd, μc ≠ μd Ha: at least one of the means is different b)In order to analyze the data with ANOVA, we need to satisfy the condition of randomization. How do we know that this condition has been met? -One SRS of batteries is selected from a collection of batteries of all brands. -The batteries are randomly allocated to the four brands. -Separate random samples of batteries are selected from each brand.
- 3. When you performed null hypothesis tests for two samples using a z-test, what can you conclude about the population growth rate of both samples under consideration if you rejected the null hypothesis?Can I have all 3 questions done, Thank you.Suppose researchers conducted a study to see if the mean body temperature for adultswas different from 98.6 degrees Fahrenheit. For this study, they took a random sampleof 25 healthy adults and found a mean body temperature of 98.2 degrees Fahrenheit forthe sample with a standard deviation of 0.6 degrees. The temperatures of the sampleparticipants were unimodal and symmetric.a. Write the null hypothesis and alternative hypothesis and define your parameter.b. Show that the necessary conditions (Randomization Condition, 10% Condition,Nearly Normal Condition) are satisfied to perform a hypothesis test. Brieflyexplain how each condition is satisfied.c. Perform the hypothesis test and find the P-value. (To show your work: Writedown which calculator you are using and what values you are entering into thecalculator.)d. Is there strong evidence that the mean body temperature is different than 98.6degrees? Briefly explain how you know.
- Suppose that we need to compute the probability of Type II error and the power for the following hypothesis test: Ho: μ = 5 and H1: μ > 5 with the following decision rule: reject Ho if [-5]/[0.1/] > 1.645 or 5 + 1.645*[0.1/] = 5.041, when we know that the true population mean is given by μ = 5.15. Then the solution should proceed as follows: Since μ = 5.15, β = P(≤xc| μ = μ*) = P(≤5.041| μ*=5.15) = P([5.15 - 5.041]//[0.1/] = P(z≤1.05) and the power of the test is given by power = 1 – .0111 = .899. Is it true or false? Note that xc is thecritical value from the appropriate sampling distribution of the sample mean, μ is the population mean under null hypothesis, μ * is the true population mean, and x-bar is the sample mean. True FalseA magazine article reported that 11% of adults buy takeout food every day. A fast-food restaurant owner surveyed 200 customers and found that 36 said that they purchased takeout food every day. At α=0.01, is there evidence to believe the article's claim? Use the P-value method with tables. Do not round intermediate steps. State the hypotheses and identify the claim with the correct hypothesis.We have specified the “tailedness” of a hypothesis test for a population mean with null hypothesis H0: μ = μ0. a. draw the ideal power curve. b. explain what your curve in part (a) portrays. left-tailed
