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 | Question AI (2024)

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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

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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 | Question AI (2)

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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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 | Question AI (2024)

FAQs

What test to use when population standard deviation is unknown? ›

A hypothesis test for a population mean when the population standard deviation,σ , is unknown is conducted in the same way as if the population standard deviation is known. The only difference is that the t-distribution is invoked instead of the standard normal distribution (z -distribution).

What test to use when standard deviation is known? ›

If the population standard deviation (σ) is known, a hypothesis test performed for one population mean is called one-mean z-test or simply z-test.

When to use z-test or t-test in statistics? ›

If the population standard deviation is known, use a z-test. If the population standard deviation is unknown, but the sample size is larger than 30, use a z-test. For small samples and unknown population standard deviations, use a t-test.

What if the population standard deviation is unknown? ›

Population Standard Deviation Unknown

If the population standard deviation, sigma is unknown, then the mean has a student's t (t) distribution and the sample standard deviation is used instead of the population standard deviation. . The t here is the t-score obtained from the Student's t table.

Can you use z-test if standard deviation is unknown? ›

If the standard deviation of the population is known and the sample size is greater than or equal to 30, the z-test can be used. Regardless of the sample size, if the population standard deviation is unknown, a t-test should be used instead.

How to find p-value when standard deviation is unknown? ›

When the population standard deviation is unknown, find the p-value (the area in the corresponding tail) for the test using the t -distribution with t=¯¯¯x−μs√n t = x ¯ − μ s n and df=n−1 d f = n − 1 . Compare the p-value to the significance level and state the outcome of the test.

When to use the t-test? ›

A t-test may be used to evaluate whether a single group differs from a known value (a one-sample t-test), whether two groups differ from each other (an independent two-sample t-test), or whether there is a significant difference in paired measurements (a paired, or dependent samples t-test).

How do you know when to use T or Z interval? ›

How to Determine When to Use a z-Distribution or a t-Distribution
  1. If the population standard deviation is known, use the z-distribution.
  2. If the population standard deviation is not known, use the t-distribution.

What are the conditions for a t-test? ›

The conditions required to conduct a t-test include the measured values in ratio scale or interval scale, simple random extraction, hom*ogeneity of variance, appropriate sample size, and normal distribution of data.

What if population standard deviation is not known? ›

Frequently, the population standard deviation (σ) is not known. We can estimate the population standard deviation (σ) with the sample standard deviation (s). However, the test statistic will no longer follow the standard normal distribution. We must rely on the student's t-distribution with n-1 degrees of freedom.

How to solve t value in statistics? ›

The t-score formula is: t = x ― − μ S n , where x ― is the sample mean, μ is the population mean, S is the standard deviation of the sample, and n is the sample size. Remember to square root n in the formula.

Can you find the population standard deviation? ›

The population standard deviation is the standard deviation of the entire population and often denoted by σ . It is given by the formula σ= ⎷1NN∑i=1(xi−μ)2 σ = 1 N ∑ i = 1 N ( x i − μ ) 2 where N is the size of the population consisting of x1,x2,… xN. x N and μ is the population mean.

How do you find the standard deviation of an unknown population? ›

When finding a confidence interval for an unknow population mean when the population standard deviation is unknown, we use the sample standard deviation s as an estimate for the (unknown) population standard deviation and we use a t -distribution with n−1 degrees of freedom to find the required t -score for the ...

Which test is correct to use if we do not know the population standard deviation? ›

Since the population standard deviation is unknown and the sample size is less than 30, the researcher should use a t-test.

What table should be used if the population variance or standard deviation is unknown? ›

If the population standard deviation is unknown, use the sample standard deviation in the confidence interval equation. To compensate for this lack of precision, use the t-statistic instead of the Z-score.

What is used when the population standard deviation is unknown and when the sample size is small? ›

The t-distribution is most useful for small sample sizes, when the population standard deviation is not known, or both. As the sample size increases, the t-distribution becomes more similar to a normal distribution.

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