Questions: Refer to the accompanying data display that results from a simple random sample of times (minutes) between eruptions of the Old Faithful geyser. The confidence level of 95% was used. Complete parts (a) and (b) below. TInterval (85.74,91.76) x̄=88.75 Sx=8.897431411 n=36 a. Express the confidence interval in the format that uses the "less than" symbol. Round the confidence interval limits given that the original times are all rounded to one decimal place. min <μ< min (Round to two decimal places as needed.)

Refer to the accompanying data display that results from a simple random sample of times (minutes) between eruptions of the Old Faithful geyser. The confidence level of 95% was used. Complete parts (a) and (b) below. TInterval (85.74,91.76) x̄=88.75 Sx=8.897431411 n=36 a. Express the confidence interval in the format that uses the "less than" symbol. Round the confidence interval limits given that the original times are all rounded to one decimal place. min <μ< min (Round to two decimal places as needed.)
Transcript text: Refer to the accompanying data display that results from a simple random sample of times (minutes) between eruptions of the Old Faithful geyser. The confidence level of $95 \%$ was used. Complete parts (a) and (b) below. TInterval \[ \begin{array}{l} (85.74,91.76) \\ \bar{x}=88.75 \\ S x=8.897431411 \\ n=36 \end{array} \] a. Express the confidence interval in the format that uses the "less than" symbol. Round the confidence interval limits given that the original times are all rounded to one decimal place. $\square$ $\square$ $\min <\mu<$ min (Round to two decimal places as needed.)
failed

Solution

failed
failed

Solution Steps

Step 1: Calculate the Margin of Error

To determine the margin of error for the confidence interval, we use the formula:

\[ \text{Margin of Error} = \frac{Z \times \sigma}{\sqrt{n}} \]

where:

  • \( Z = 1.96 \) (the Z-score for a 95% confidence level),
  • \( \sigma = 8.897431411 \) (the sample standard deviation),
  • \( n = 36 \) (the sample size).

Substituting the values, we have:

\[ \text{Margin of Error} = \frac{1.96 \times 8.897431411}{\sqrt{36}} = 2.91 \]

Step 2: Determine the Confidence Interval

The confidence interval for the population mean \( \mu \) is calculated using the sample mean and the margin of error:

\[ \bar{x} - \text{Margin of Error} < \mu < \bar{x} + \text{Margin of Error} \]

Substituting the values:

\[ 88.75 - 2.91 < \mu < 88.75 + 2.91 \]

Calculating the limits:

\[ 85.84 < \mu < 91.66 \]

Final Answer

The confidence interval can be expressed as:

\[ \boxed{85.84 < \mu < 91.66} \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Preparing the Sodium Hydroxide Solution (Secondary Standard) Calculate the volume (mL) of 6 M NaOH required to prepare 600 mL of 0.1 M NaOH. Report your answer to three significant figures. Volume of 6 M NaOH required (mL)
failedAnswered
Find the standard deviation, s, of sample data summarized in the frequency distribution table below by using the formula below, where x represents the class midpoint, f represents the class frequency, and n represents the total number of sample values. Also, compare the computed standard deviation to the standard deviation obtained from the original list of data values, 11.1. s = sqrt((n[Σ(f * x^2)] - [Σ(f * x)]^2) / (n(n-1))) Interval 30-36 37-43 44-50 51-57 58-64 65-71 72-78 Frequency 2 2 6 4 9 32 38 Standard deviation = (Round to one decimal place as needed.)
failedAnswered
Ramer and Knox began a partnership by investing 60,000 and 90,000, respectively. The partners agreed to share net income and loss by giving annual salary allowances of 50,000 to Ramer and 40,000 to Knox, 10% interest allowances on their investments, and any remaining balance shared equally. Note: Enter all allowances as positive values. Enter losses as negative values. Required: 1. Determine each partner's share given a first-year net income of 98,800. 2. Determine each partner's share given a first-year net loss of 16,800.
failedAnswered
Apex Learning - Courses com/public/activity/5005003/assessment 5.5.3 Test (CST): Descriptive Statistics Question 2 of 25 A snack bar offers chili and/or cheese on its hot dogs for an additional fee. The owner kept track of the hot dog orders over the course of a week. His data are shown in a relative frequency table. Cheese No cheese Total Chill 0.1 0.3 0.4 No chill 0.2 0.4 0.6 Total 0.3 0.7 1.0 What does the 0.2 in the highlighted cell mean? A. 20% of his customers ordered cheese but no chili on their hot dog. B. 20% of the customers that ordered cheese did not order chili. C. 20% of his customers ordered cheese on their hot dog. D. 20% of his customers did not order chili on their hot dog.
failedAnswered
Um motor de potência útil igual a 125 W, fazendo funcionar um elevador vertical, eleva a 10 m de altura, com velocidade constante, um corpo de peso igual a 50 N. Determine o tempo gasto para o elevador subir esse corpo nas condições da situação descrita. Uma pequena rocha de 2 kg se desprende do alto de um desfiladeiro. Ao passar pelo ponto que a rocha está a 15 metros do solo a rocha está com 72 km/h. No momento descrito, calcule a energia potencial gravitacional e a energia cinética da rocha. Use g=10 m/s^2