1.
An oceanographer wants to test, on the basis of
a random sample size of 20, whether the average depth of the ocean in certain
areas is greater than 75 fathoms. A the .10 level of significance, what will
the oceanographer decide if she observes a sample mean of 75.5? Assume that the
population standard deviation is 1.75. (Also, compute the p-value)

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We have

Null Hypothesis:u=75 fathom

Alternative Hypothesis:u>75 fathom

Given mean,m=75.5

Standard deviation,d =1.75

Sample size,n=20

Calculating the test statistic:

The degree of freedom =20-1=19,

The critical value corresponding to .1 significance level is 3.8834

The p value corresponding to t=1.278 and degree of freedom is ..1083

As the p value is greater than the significance level therefore we accept the null hypothesis and accept that the average depth in the certain ocean is not greater than 75 fathom.

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