3.
Hypotheses are:
Since population standard deviation is unknown and hypothesis test population mean so t test should be used. Here sample size is large so we can assume that sampling distribution of sample mean is normal.
So test statitics will be
Here test is two tailed and degree of freedom of the test is df=n-1=10-1=9. So for , critical value of the test are +/-2.2622. Rejection region:
If t< -2.2622 or t > 2.2622, we reject the null hypothesis.
Since test statistics value is not less than -2.2622 so we fail to reject the null hypothesis.
That is we cannot conclude that spring constant is different from 10 kN/m.
4:
Since there 50 data values in the sample so degree of freedom is df=50-1=49 and critical value of t for 95% confidence interval is +/- 2.0096. Therefore required confidence interval is
Therefore, a 95% confidence interval for the mean is (9.62138, 10.00938).
--------------------------
Hypotheses are:
Since population standard deviation is unknown and hypothesis test population mean so t test should be used. Here sample size is large so we can assume that sampling distribution of sample mean is normal.
So test statitics will be
Here test is two tailed and degree of freedom of the test is df=n-1=50-1=49. So for , critical value of the test are +/-2.0096. Rejection region:
If t< -2.0096 or t > 2.0096, we reject the null hypothesis.
Since test statistics value is less than -2.0096 so we reject the null hypothesis.
That is we can conclude that spring constant is different from 10 kN/m.
10 springs have been tested and have had their spring constant recorded. This data has been...
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