In a similar study using the same design (sample of n = 9 participants), the individuals who wore the shirt produced an average estimate of M = 6.4 with SS = 162.

Lewis Harvey 2020-11-08 Answered

In a similar study using the same design (sample of \(n = 9\) participants), the individuals who wore the shirt produced an average estimate of \(M = 6.4\) with \(SS = 162\).
The average number who said they noticed was (population mean) 3.1. Calculate a One Sample t-test using a two-tailed test with \(\displaystyle\alpha={.05}\).

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Elberte
Answered 2020-11-09 Author has 27522 answers

Step 1
The null and alternative hypotheses are’
\(\displaystyle{H}_{{0}}:{m}={3.1}\)
\(\displaystyle{H}_{{1}}:{m}\ne{3.1}\)
The sample mean is 6.4 and the population mean is 3.1.
Here, \(SS=162\) and \(n=9\). The estimate of the standard deviation is
\(\displaystyle{s}=\sigma-\cap=\sqrt{{\frac{{{S}{S}}}{{{n}-{1}}}}}\).
Therefore, the \(\displaystyle{s}=\sqrt{{\frac{{162}}{{8}}}}={4.5}\).
Test statistic:
The test statistic for hypothesis test for mean is given by:
\(\displaystyle{t}=\frac{{{x}-\overline{-}\mu}}{{\frac{{s}}{\sqrt{{{n}}}}}}\)
\(\displaystyle=\frac{{{6.4}-{3.1}}}{{\frac{{4.5}}{\sqrt{{{9}}}}}}\)
\(= 2.2\)
The test statistic is 2.2.
Step 2
Critical value:
Here, sample size is 9.
Thus, the degrees of freedom for the test is \(8(=9-1)\).
Therefore, the df is 15.
The critical value is \(\displaystyle\pm{2.306}\) using the excel formula “=(T.INV.2T(0.05,8))”
Decision rule:
Denote t as test statistic value and \(\displaystyle{t}_{{\frac{\alpha}{{2}}}}\) as the critical value.
Decision rule based on critical approach:
If \(\displaystyle{t}\le–{t}_{{\frac{\alpha}{{2}}}}{\left({\quad\text{or}\quad}\right)}{t}\ge{t}_{{\frac{\alpha}{{2}}}}\), then reject the null hypothesis \(\displaystyle{H}_{{0}}\).
If \(\displaystyle-{t}_{{\frac{\alpha}{{2}}}}{<}{t}{<}{t}_{{\frac{\alpha}{{2}}}}\), then fail to reject the null hypothesis \(\displaystyle{H}_{{0}}\).
Conclusion:
The test statistic value is given as 2.2 and critical value is \(\displaystyle\pm{2.306}\).
Here, \(-2.306<2.2<2.306\).
By the rejection rule fail to reject \(\displaystyle{H}_{{0}}\).
The test statistic value is 2.2.
The critical/cut off values is \(\displaystyle\pm{2.131}\)

Not exactly what you’re looking for?
Ask My Question
28
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-05-22
Are Toyota or Nissan owners more satisfied with their vehicles? Let's design a study to find out. We'll select a random sample of 400 Toyota owners and a separate random sample of 400 Nissan owners. Then we'll ask each individual in the sample: "Would you say that you are generally satisfied with your (Toyota/Nissan) vehicle?" What type of study design is being used to produce data?
asked 2020-11-08

A researcher is conducting a study to examine the effects of cognitive behavior therapy for the treatment of social anxiety in a sample of 16 participants. He measures the social anxiety scores of participants before the tratment and then again after treatment and the resulting data is as follows:
\(n=16, M_0=5, s =4\)
a) What type of design is this study (single-sample, independent measures, repeated measures)
b)State the null and alternate hypotheses
c) Using an \(\displaystyle\alpha\ level\ of\ {.05}{\left(\alpha={.05}\right)}\), identify the critical values of t for a 2-tailed test.

asked 2021-06-16
Refer to the Journal of Experimental Social Psychology (Vol. 45, 2009) study of whether buying gifts truly buys love. Recall that study participants were randomly assigned to play the role of gift giver or gift receiver. Gift receivers were asked to provide the level of appreciation (measured on a 7-point scale where 1 = "not at all" and 7 = "to a great extent") they had for the last birthday gift they received from a loved one. Gift givers were asked to recall the last birthday gift they gave to a loved one and to provide the level of appreciation the loved one had for the gift. The researchers wanted to know if the average level of appreciation is higher for birthday gift givers than for birthday gift receivers. a. Why is this study designed? b. Specify the key elements of the study: experimental unit, response variable, factor, and treatments.
asked 2021-06-10
Can filling car tires with nitrogen instead of compressed air increase gas mileage? Describe how you would design a study to try to answer this question. Be as specific as you can about the details of your study.
asked 2021-05-21
A proposed study design is to leave 100 questionnaires by the checkout line in a student cafeteria. The questionnaire can be picked up by any student and returned to the cashier. Explain why this volunteer sample is a poor study design.
asked 2021-06-21
An observational study is retrospective if it considers only existing data. It is prospective if the study design calls for data to be collected as time goes on. Tell which of the following observational studies are retrospective and which are prospective. Paxton devises a complicated formula based on game statistics for rating quarterbacks. He applies it to all NFL quarterbacks who played in the league between 1950 and 2000 and concludes that the quarterbacks from the 1970s were the best overall.
asked 2021-06-21
An observational study is retrospective if it considers only existing data. It is prospective if the study design calls for data to be collected as time goes on. Tell which of the following observational studies are retrospective and which are prospective. Paxton devises a complicated formula based on game statistics for rating quarterbacks. He applies it to all NFL quarterbacks who played in the league between 1950 and 2000 and concludes that the quarterbacks from the 1970s were the best overall.
...