Need the answers to Parts (a) thru (e). Please solve by hand (I can\'t use compu

Question

Need the answers to Parts (a) thru (e). Please solve by hand (I can't use computers in class) and show all work so I can study the material. Thank you very much for the help!

3. We manufacture rubber Sealant o-rings for SpaceX. In a batch of N 100, we measure the coldest temperature at which each o-ring is still safe to use. We obtain the average temperature T 40(F) and standard deviation S 0.8. The morning of a launch is 53.5 (F). As one of many components to our decision making process, we test the null hypothesis Ho pr 53.5 against the one-sided alternative hypothesis Ha T 53.5; if the null hypothesis is rejected, we consider this to be evidence that we should not launch. We set our confidence high (i.e. significance low a 0.01, so that we can be very sure of our results. (a) How many degrees of freedom will our T test statistic have? (b) Use the T table to find the critical value TN-1,a. Since the T distribution is symmetric, TN-1,1-o N-1, T-53.5 c) Compute the test statistic T (d) Is -T T? Do we reject the null hypothesis? Explain and justify. N-1,a (e) On the T-table, what is the approximate p-value of our data?

Explanation / Answer

a)here degree of freedom =n-1=99

b) from t table at 0.01 level and 99 degree of freedom , for right tailoed test critical value of t=2.3646

c)here std error =std deviation/(n)1/2 =0.08

hence test stat t=(54-53.5)/0.08=6.25

d) YEs, we reject null hypothesis

e) p value for above test stat=0.0000

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