Thanks to an initiative to recruit top students, an administrator at a college claims that this year's entering class must have a greater mean IQ score than that of entering classes from previous years. The administrator tests a random sample of 15 of this year's entering students and finds that their mean IQ score is 118, with a standard deviation of 14. The college records indicate that the mean IQ score for entering students from previous years is 114. Is there enough evidence to conclude, at the 0.05 level of significance, that the population mean IQ score, μ, of this year's class is greater than that of previous years? To answer, assume that the IQ scores of this year's entering class are approximately normally distributed. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. A. Find the value of the test statistic and round to 3 or more decimal places. (I have posted a picture of an example problem and the equation to use, with the correct answer as every expert I have asked thus far has gotten this problem wrong.) B. Find the critical value. (Round to three or more decimal places.) C. Can we conclude that the mean IQ score of this year's class is greater than that of previous years?

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Thanks to an initiative to recruit top students, an administrator at a college claims that this year's entering class must have a greater mean IQ score than that of entering classes from previous years. The administrator tests a random sample of 15 of this year's entering students and finds that their mean IQ score is 118, with a standard deviation of 14. The college records indicate that the mean IQ score for entering students from previous years is 114. Is there enough evidence to conclude, at the 0.05 level of significance, that the population mean IQ score, μ, of this year's class is greater than that of previous years? To answer, assume that the IQ scores of this year's entering class are approximately normally distributed. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places.

A. Find the value of the test statistic and round to 3 or more decimal places. (I have posted a picture of an example problem and the equation to use, with the correct answer as every expert I have asked thus far has gotten this problem wrong.)

B. Find the critical value. (Round to three or more decimal places.)

C. Can we conclude that the mean IQ score of this year's class is greater than that of previous years?   

(c) Finding the value of the test statistic
Since we're assuming the null is true, we use μ = 36. We also have that x = 32, s = 11, and n = 14. So we get the following.
32-36
11
✓√14
t
x-μ
S
√n
≈ 1.361
Transcribed Image Text:(c) Finding the value of the test statistic Since we're assuming the null is true, we use μ = 36. We also have that x = 32, s = 11, and n = 14. So we get the following. 32-36 11 ✓√14 t x-μ S √n ≈ 1.361
The Journal de Botanique reported that the mean height of Begonias grown while being treated with a
particular nutrient is 36 centimeters. To check whether this is still accurate, heights are measured for a
random sample of 14 Begonias grown while being treated with the nutrient. The sample mean and sample
standard deviation of those height measurements are 32 centimeters and 11 centimeters, respectively.
Assume that the heights of treated Begonias are approximately normally distributed. Based on the sample,
can it be concluded that the population mean height of treated begonias, µ, is different from that reported in
the journal? Use the 0.10 level of significance. Perform a two-tailed test. Then complete the parts below. Carry
your intermediate computations to three or more decimal places.
MATL
BU
Ch
Transcribed Image Text:The Journal de Botanique reported that the mean height of Begonias grown while being treated with a particular nutrient is 36 centimeters. To check whether this is still accurate, heights are measured for a random sample of 14 Begonias grown while being treated with the nutrient. The sample mean and sample standard deviation of those height measurements are 32 centimeters and 11 centimeters, respectively. Assume that the heights of treated Begonias are approximately normally distributed. Based on the sample, can it be concluded that the population mean height of treated begonias, µ, is different from that reported in the journal? Use the 0.10 level of significance. Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. MATL BU Ch
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