The provided sample mean is "\\overline{X} =1446" and the sample standard deviation is "s=56", and the sample size is "n=43."
The following null and alternative hypotheses need to be tested:
This corresponds to a two-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used.
Based on the information provided, the significance level is "\\alpha=0.1," and the critical value for a two-tailed test is "t_c=1.682."
The rejection region for this two-tailed test is "R=\\{{t: |t|>1.682}\\}"
The t-statistic is computed as follows:
Since it is observed that "|t|=25.0588>t_c=1.682," |t| = 25.059 it is then concluded that the null hypothesis is rejected.
Using the P-value approach: The p-value is "p=0," and since "p=0<0.1," it is concluded that the null hypothesis is rejected.
Conclusion
It is concluded that the null hypothesis "H_0" is rejected. Therefore, there is enough evidence to claim that the population mean "\\mu" is different than 1660, at the 0.1 significance level.
The 90% confidence interval is
"1431.636<\\mu<1460.364"
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