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

Lewis Harvey

Answered question

2020-11-08

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 α=.05.

Answer & Explanation

Elberte

Elberte

Skilled2020-11-09Added 95 answers

Step 1
The null and alternative hypotheses are’
H0:m=3.1
H1:m3.1
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
s=σ-=SSn-1.
Therefore, the s=1628=4.5.
Test statistic:
The test statistic for hypothesis test for mean is given by:
t=x--¯μsn
=6.4-3.14.59
=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 ±2.306 using the excel formula “=(T.INV.2T(0.05,8))”
Decision rule:
Denote t as test statistic value and tα2 as the critical value.
Decision rule based on critical approach:
If ttα2  or  ttα2, then reject the null hypothesis H0.
If -tα2<t<tα2, then fail to reject the null hypothesis H0.
Conclusion:
The test statistic value is given as 2.2 and critical value is ±2.306.
Here, -2.306<2.2<2.306.
By the rejection rule fail to reject H0.
The test statistic value is 2.2.
The critical/cut off values is ±2.131

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