b) t=2.179 d) t=3.055 _ 13) If the population standard deviation is unknown, what test statistic is to be used? a) t -test b) z -test c) population mean d) standard deviation _14) A tire manufacturer claims that its tires have a mean life of 40,000km . A random sample of 46 of these tires is tested and the sample mean is 38,000km . Assume that the population's standard deviation is 2,000km and the lives of the tires are approximately normally distributed. Determine the computed value at 5% level of significance. a) -6.782 b) -3.033 c) 3.033 d) 6.782 For items. 15 - 17 , refer to the given problem below: The Choco Toppings, Inc. is one of the manufacturers of chocolate toppings which uses a machine to dispense liquid ingredients into bottles that move along a filling line. The owner claims that the machine can dispense at an average of 50 grams with a standard deviation of 0.7 grams. A sample of 35 bottles was selected and it was found out that the average amount dispensed in the sample is 49.3 grams. Test the claims of the owner of the company at 5% level of significance. qquad 15) Which of the following information is correct? a) a=0.5 c) bar(x)=35 b) sigma=0.7 d) mu=49.3 16) What test statistic will be used? a) t -test c) population mean b) z -test d) standard deviation qquad 17) Find the computed value. a) -5.916 b) -4.950 c) 4.950 d) 5.916 qquad 18) What should be the decision if the computed z -value lies in the critical region? a) reject the null hypothesis. b) reject the alternative hypothesis. c) Do not reject the null hypothesis. d) Do not reject the alternative hypothesis. qquad 19) If the t-computed value is 1.093 and the critical value is 1.699 , what will be the decision? a) reject the null hypothesis. b) support the null hypothesis
Question
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Cynthia LopezVeteran · Tutor for 12 years
Answer
13) a) t-test<br /> 14) b) -3.033<br /> 15) b) σ=0.7<br /> 16) b) z-test<br /> 17) b) -4.950<br /> 18) a) reject the null hypothesis.<br /> 19) c) Do not reject the null hypothesis.
Explanation
<br />13) When the population standard deviation is unknown, taking into account a sample's measure of standard deviation, for statistical hypothesis testing we usually use the t-test.<br />14) We calculate the test-statistic based on means/population deviations. That's a usual z-test practice. The calculated z-score for the provided case is -3.033 falling in a rejection region at 5% level of significance.<br />15) We only have information about σ (standard deviation) which is 0.7.<br />16) In such scenarios where we have the population standard deviation and sampling distribution is normal, z-test should be used.<br />17) As per our test using z-test, we get the computed value to be -4.950.<br />18) Whenever our calculated statistic lies in the critical region, it's an indicator of a significant event. So, we reject the null hypothesis that the mean grams poured per bottle is 50 grams.<br />19) However, in this case, t (1.093) < critical value (1.699) here. Since the computed value is less than the critical value, we fail to reject our null hypothesis in the scenario provided.
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