Questions: Hypothesis Test Description [Items 25 - 30] A sample of 100 UMD freshmen takes a university readiness assessment and the sample mean is M=54. If the mean for all college freshmen on this test is μ=50 and σ=15, can you conclude that this UMD sample is significantly different from the population? Use a two-tailed test with α=0.05. TIP: Sketch the distribution. Show your work for calculating the standard error and the obtained z-score test statistic. 26 1 point What is/are the critical z-score values that define(s) the boundary of the critical region in this study? zcrit= z=+1.96 z=+2.58 z= ± 2.58 z= ± 1.96 27 1 point NOTE: Provide a numerical answer with TWO decimal places; you should include extra "O"s if needed to reach TWO decimal places (0.00). What is the value of the standard error, σM, for this study? Type your answer- 28 1 point NOTE: Provide a numerical answer with TWO decimal places; you should include extra "O"s if needed to reach TWO decimal places ( 0.00 ). What is the value of the obtained z-score ( zobt test statistic) for this study? Type your answer. 29 0.5 points Based on the results of this study, what decision about the null hypothesis should the researcher make? Reject H0 Fail to reject H0

Hypothesis Test Description [Items 25 - 30] A sample of 100 UMD freshmen takes a university readiness assessment and the sample mean is M=54. If the mean for all college freshmen on this test is μ=50 and σ=15, can you conclude that this UMD sample is significantly different from the population? Use a two-tailed test with α=0.05. TIP: Sketch the distribution. Show your work for calculating the standard error and the obtained z-score test statistic. 26 1 point What is/are the critical z-score values that define(s) the boundary of the critical region in this study? zcrit= z=+1.96 z=+2.58 z= ± 2.58 z= ± 1.96 27 1 point NOTE: Provide a numerical answer with TWO decimal places; you should include extra "O"s if needed to reach TWO decimal places (0.00). What is the value of the standard error, σM, for this study? Type your answer- 28 1 point NOTE: Provide a numerical answer with TWO decimal places; you should include extra "O"s if needed to reach TWO decimal places ( 0.00 ). What is the value of the obtained z-score ( zobt test statistic) for this study? Type your answer. 29 0.5 points Based on the results of this study, what decision about the null hypothesis should the researcher make? Reject H0 Fail to reject H0
Transcript text: Hypothesis Test Description [Items 25 - 30] A sample of 100 UMD freshmen takes a university readiness assessment and the sample mean is $M=54$. If the mean for all college freshmen on this test is $\mu=50$ and $\sigma=15$, can you conclude that this UMD sample is significantly different from the population? Use a two-tailed test with $\alpha=0.05$. TIP: Sketch the distribution. Show your work for calculating the standard error and the obtained $z$-score test statistic. 26 1 point What is/are the critical $z$-score values that define(s) the boundary of the critical region in this study? $z_{\text {crit }}=$ $\qquad$ $z=+1.96$ $z=+2.58$ $z= \pm 2.58$ $z= \pm 1.96$ 27 1 point NOTE: Provide a numerical answer with TWO decimal places; you should include extra "O"s if needed to reach TWO decimal places $(0.00)$. What is the value of the standard error, $\sigma_{M}$, for this study? Type your answer- 28 1 point NOTE: Provide a numerical answer with TWO decimal places; you should include extra "O"s if needed to reach TWO decimal places ( 0.00 ). What is the value of the obtained $z$-score ( $z_{\mathrm{obt}}$ test statistic) for this study? Type your answer. 29 0.5 points Based on the results of this study, what decision about the null hypothesis should the researcher make? Reject $\mathrm{H}_{0}$ Fail to reject $\mathrm{H}_{0}$
failed

Solution

failed
failed

Solution Steps

Step 1: Critical z-score Values

For a two-tailed hypothesis test with a significance level of \( \alpha = 0.05 \), the critical z-scores that define the boundaries of the critical region are given by \( z_{\text{crit}} = \pm 1.96 \).

Step 2: Calculate Standard Error

The standard error of the sample mean \( \sigma_M \) is calculated using the formula: \[ \sigma_M = \frac{\sigma}{\sqrt{n}} = \frac{15}{\sqrt{100}} = 1.50 \]

Step 3: Calculate Obtained z-score

The obtained z-score \( z_{\text{obt}} \) is calculated using the formula: \[ z_{\text{obt}} = \frac{M - \mu}{\sigma_M} = \frac{54 - 50}{1.50} = 2.67 \]

Step 4: Decision about the Null Hypothesis

To determine whether to reject the null hypothesis \( H_0 \), we compare the obtained z-score with the critical z-scores:

  • If \( |z_{\text{obt}}| > z_{\text{crit}} \), we reject \( H_0 \).
  • Here, \( |2.67| > 1.96 \), thus we reject \( H_0 \).

Final Answer

The critical z-score values are \( \pm 1.96 \), the standard error is \( 1.50 \), the obtained z-score is \( 2.67 \), and the decision is to reject the null hypothesis.

\[ \boxed{\text{Critical z-scores: } \pm 1.96, \, \sigma_M = 1.50, \, z_{\text{obt}} = 2.67, \, \text{Decision: Reject } H_0} \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
One hundred volunteers were divided into two equal-sized groups. Each volunteer took a math test that involved transforming strings of eight digits into a new string that fit a set of given rules, as well as a third, hidden rule. Prior to taking the test, one group received 8 hours of sleep, while the other group stayed awake all night. The scientists monitored the volunteers to determine whether and when they figured out the rule. Of the volunteers who slept, 38 discovered the rule; of the volunteers who stayed awake, 15 discovered the rule. What can you infer about the proportions of volunteers in the two groups who discover the rule? Support your answer with a 90% confidence interval. Let p̂1 be the proportion of volunteers who figured out the third rule in the group that slept and let p̂2 be the proportion of volunteers who figured out the third rule in the group that stayed awake all night. The 90% confidence interval for (p1-p2) is , (Round to the nearest thousandth as needed.)
failedAnswered
a. Use a graphing utility to graph (y=x^2-73 x+700) in a standard viewing rectangle. What do you observe? b. Find the coordinates of the vertex for the given quadratic function. c. Find a viewing rectangle that will give a relatively complete picture of the parabola. d. In general, explain how knowing the coordinates of a parabola's vertex can help determine a reasonable viewing rectangle on a graphing utility for obtaining a complete picture of the parabola. a. What do you observe in the standard viewing rectangle? b. The coordinates of the vertex are . (Type an ordered pair.)
failedAnswered
Use the Rational Zero Theorem to list all possible rational zeros for the given function. f(x)=x^3-2x^2-13x+14 Choose the answer below that lists all possible rational zeros. A. -1,1,-2,2,-7,7,-14,14,-1/2, 1/2,-1/7, 1/7,-1/14, 1/14 B. -1,1,-14,14 C. -1,1,-2,2,-7,7,-14,14 D. -1,1,-1/2, 1/2,-1/7, 1/7,-1/14, 1/14
failedAnswered
VA = 5,000, l = (1+0.07)^5
failedAnswered
A flat, thin structure made of dense connective tissue that serves to attach a muscle to a bone (or another muscle) is called a(n) ... - perimysium - myolemma - aponeurosis - tendon