StatTutor Lesson - The One-Sample t Confidence Interval

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The one-sample t confidence interval
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      Question 1

      96

      Question 1.

      What do we use as a multiplier in a confidence interval estimate of µ when σ is unknown?

      		A.
      		B.
      Incorrect. We use t*, not z* as the multiplier in a confidence interval estimate of µ when σ is unknown.
      Correct. We use t*, not z* as the multiplier in a confidence interval estimate of µ when σ is unknown.
      Incorrect. Try again.
      2

      Question 2

      158

      Question 2.

      Where do we find t* in table C, the t distribution table?

      		A.
      		B.
      		C.
      Incorrect. Most of the values on the t table are t* values. A particular t* value is found in the intersection of the appropriate level of confidence column and the appropriate degrees of freedom row.
      Correct. Most of the values on the t table are t* values. A particular t* value is found in the intersection of the appropriate level of confidence column and the appropriate degrees of freedom row.
      Incorrect. Try again.
      2

      Question 3

      201

      Question 3.

      If the actual degrees of freedom are not found on the t table, what should you do?

      		A.
      		B.
      		C.
      Incorrect. Find the df closest to the actual without going over the actual.
      Correct. Find the df closest to the actual without going over the actual.
      Incorrect. Try again.
      2

      Question 4

      356

      Question 4.

      What is the basic difference between a one-sample t procedure using s as an estimate of σ and a one-sample z procedure with σ known?

      		A.
      		B.
      		C.
      Incorrect. Basically, we use the t table and t-values rather than standard Normal values.
      Correct. Basically, we use the t table and t-values rather than standard Normal values.
      Incorrect. Try again.
      2

      Question 5

      399

      Question 5.

      What parameter needs to be estimated?

      		A.
      		B.
      		C.
      		D.
      Incorrect. The parameter estimated with a one-sample t procedure is the mean response of all individuals. In this case, the parameter is the mean resting pulse rate of all male students.
      Correct. The parameter estimated with a one-sample t procedure is the mean response of all individuals. In this case, the parameter is the mean resting pulse rate of all male students.
      Incorrect. Try again.
      2

      Question 6

      447

      Question 6.

      Are there any outliers in this plot of resting pulse rates?

      		A.
      		B.
      Incorrect. There are no observations were you would say, “Oh, wow!! That’s an outlier!”
      Correct. There are no observations were you would say, “Oh, wow!! That’s an outlier!”
      Incorrect. Try again.
      2

      Question 7

      463

      Question 7.

      For these data, can we apply the Central Limit Theorem?

      		A.
      		B.
      Incorrect. The sample size is 92 and the data were collected with an SRS, so yes, we can apply the Central Limit Theorem.
      Correct. The sample size is 92 and the data were collected with an SRS, so yes, we can apply the Central Limit Theorem.
      Incorrect. Try again.
      2

      Question 8

      470

      Question 8.

      Which formula should we use to find the confidence interval estimate for µ?

      		A.
      		B.
      Incorrect. Since we don’t know σ and will use s to estimate it, we need to use the formula with t*.
      Correct. Since we don’t know σ and will use s to estimate it, we need to use the formula with t*.
      Incorrect. Try again.
      2

      Question 9

      492

      Question 9.

      The actual degrees of freedom are df = 91. The following degrees of freedom are given on the t table. Which df row should we use to find t*?

      		A.
      		B.
      		C.
      		D.
      Incorrect. Use the closest df without going over. 80 is the closest to 91 that is still smaller than 91 so we use 80 df to find t*.
      Correct. Use the closest df without going over. 80 is the closest to 91 that is still smaller than 91 so we use 80 df to find t*.
      Incorrect. Try again.
      2

      Questions 10-11

      546

      Question 10.

      What is the name for the value 2.28?

      		A.
      		B.
      		C.
      Incorrect. 2.28 is the margin of error.
      Correct. 2.28 is the margin of error.
      Incorrect. Try again.
      2

      Question 12

      560

      Question 12.

      True or false: We must always use a t-distribution whenever s is used to estimate σ.

      		A.
      		B.
      Incorrect. This is a true statement.
      Correct. This is a true statement.
      Incorrect. Try again.
      2